/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 237 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 3 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (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), 86 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 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), 29 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), 2 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), 11 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 18 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 130 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 54 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 12 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (96) CdtProblem (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 63 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 52 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 224 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 114 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 54 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 354 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 74 ms] (156) CdtProblem (157) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (164) CdtProblem (165) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 4 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 281 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (170) 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(app(if, true), xs), ys) -> xs app(app(app(if, false), xs), ys) -> ys app(app(sub, x), 0) -> x app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y) app(app(gtr, 0), y) -> false app(app(gtr, app(s, x)), 0) -> true app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y) app(app(d, x), 0) -> true app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) app(len, nil) -> 0 app(len, app(app(cons, x), xs)) -> app(s, app(len, xs)) app(app(filter, p), nil) -> nil app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter ---------------------------------------- (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(app(if, true), xs), ys) -> xs app(app(app(if, false), xs), ys) -> ys app(app(sub, x), 0) -> x app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y) app(app(gtr, 0), y) -> false app(app(gtr, app(s, x)), 0) -> true app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y) app(app(d, x), 0) -> true app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) app(len, nil) -> 0 app(len, app(app(cons, x), xs)) -> app(s, app(len, xs)) app(app(filter, p), nil) -> nil app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) The (relative) TRS S consists of the following rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter 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(app(if, true), xs), ys) -> xs app(app(app(if, false), xs), ys) -> ys app(app(sub, x), 0) -> x app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y) app(app(gtr, 0), y) -> false app(app(gtr, app(s, x)), 0) -> true app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y) app(app(d, x), 0) -> true app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) app(len, nil) -> 0 app(len, app(app(cons, x), xs)) -> app(s, app(len, xs)) app(app(filter, p), nil) -> nil app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) The (relative) TRS S consists of the following rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(app(if, true), xs), ys) -> xs app(app(app(if, false), xs), ys) -> ys app(app(sub, x), 0) -> x app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y) app(app(gtr, 0), y) -> false app(app(gtr, app(s, x)), 0) -> true app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y) app(app(d, x), 0) -> true app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) app(len, nil) -> 0 app(len, app(app(cons, x), xs)) -> app(s, app(len, xs)) app(app(filter, p), nil) -> nil app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) The (relative) TRS S consists of the following rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter Rewrite Strategy: INNERMOST ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(app(if, true), xs), ys) -> xs app(app(app(if, false), xs), ys) -> ys app(app(sub, x), 0') -> x app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y) app(app(gtr, 0'), y) -> false app(app(gtr, app(s, x)), 0') -> true app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y) app(app(d, x), 0') -> true app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) app(len, nil) -> 0' app(len, app(app(cons, x), xs)) -> app(s, app(len, xs)) app(app(filter, p), nil) -> nil app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) The (relative) TRS S consists of the following rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0') -> 0' encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0' encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: app(app(app(if, true), xs), ys) -> xs app(app(app(if, false), xs), ys) -> ys app(app(sub, x), 0') -> x app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y) app(app(gtr, 0'), y) -> false app(app(gtr, app(s, x)), 0') -> true app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y) app(app(d, x), 0') -> true app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) app(len, nil) -> 0' app(len, app(app(cons, x), xs)) -> app(s, app(len, xs)) app(app(filter, p), nil) -> nil app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0') -> 0' encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0' encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter Types: app :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app if :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app true :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app false :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app sub :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app 0' :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app s :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app gtr :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app d :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app len :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app nil :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app cons :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app filter :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encArg :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app cons_app :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_app :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_if :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_true :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_false :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_sub :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_0 :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_s :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_gtr :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_d :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_len :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_nil :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_cons :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_filter :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app hole_if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app1_3 :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app gen_if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app2_3 :: Nat -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: app, encArg They will be analysed ascendingly in the following order: app < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: app(app(app(if, true), xs), ys) -> xs app(app(app(if, false), xs), ys) -> ys app(app(sub, x), 0') -> x app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y) app(app(gtr, 0'), y) -> false app(app(gtr, app(s, x)), 0') -> true app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y) app(app(d, x), 0') -> true app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) app(len, nil) -> 0' app(len, app(app(cons, x), xs)) -> app(s, app(len, xs)) app(app(filter, p), nil) -> nil app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0') -> 0' encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0' encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter Types: app :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app if :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app true :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app false :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app sub :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app 0' :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app s :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app gtr :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app d :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app len :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app nil :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app cons :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app filter :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encArg :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app cons_app :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_app :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_if :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_true :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_false :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_sub :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_0 :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_s :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_gtr :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_d :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_len :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_nil :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_cons :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app encode_filter :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app hole_if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app1_3 :: if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app gen_if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app2_3 :: Nat -> if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app Generator Equations: gen_if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app2_3(0) <=> if gen_if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app2_3(+(x, 1)) <=> cons_app(if, gen_if:true:false:sub:0':s:gtr:d:len:nil:cons:filter:cons_app2_3(x)) The following defined symbols remain to be analysed: app, encArg They will be analysed ascendingly in the following order: app < encArg ---------------------------------------- (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(app(if, true), xs), ys) -> xs app(app(app(if, false), xs), ys) -> ys app(app(sub, x), 0) -> x app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y) app(app(gtr, 0), y) -> false app(app(gtr, app(s, x)), 0) -> true app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y) app(app(d, x), 0) -> true app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) app(len, nil) -> 0 app(len, app(app(cons, x), xs)) -> app(s, app(len, xs)) app(app(filter, p), nil) -> nil app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter 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(len, nil) -> 0 app(c_app(d, x), 0) -> true app(c_app(c_app(if, false), xs), ys) -> ys app(c_app(gtr, 0), y) -> false app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) app(c_app(filter, p), nil) -> nil app(c_app(gtr, c_app(s, x)), 0) -> true app(c_app(sub, x), 0) -> x app(c_app(gtr, c_app(s, x)), c_app(s, y)) -> app(app(gtr, x), y) app(c_app(sub, c_app(s, x)), c_app(s, y)) -> app(app(sub, x), y) app(c_app(c_app(if, true), xs), ys) -> xs app(len, c_app(c_app(cons, x), xs)) -> app(s, app(len, xs)) app(c_app(filter, p), c_app(c_app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) The (relative) TRS S consists of the following rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter 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(len, nil) -> 0 [1] app(c_app(d, x), 0) -> true [1] app(c_app(c_app(if, false), xs), ys) -> ys [1] app(c_app(gtr, 0), y) -> false [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) [1] app(c_app(filter, p), nil) -> nil [1] app(c_app(gtr, c_app(s, x)), 0) -> true [1] app(c_app(sub, x), 0) -> x [1] app(c_app(gtr, c_app(s, x)), c_app(s, y)) -> app(app(gtr, x), y) [1] app(c_app(sub, c_app(s, x)), c_app(s, y)) -> app(app(sub, x), y) [1] app(c_app(c_app(if, true), xs), ys) -> xs [1] app(len, c_app(c_app(cons, x), xs)) -> app(s, app(len, xs)) [1] app(c_app(filter, p), c_app(c_app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) [1] encArg(if) -> if [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(sub) -> sub [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(gtr) -> gtr [0] encArg(d) -> d [0] encArg(len) -> len [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [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_if -> if [0] encode_true -> true [0] encode_false -> false [0] encode_sub -> sub [0] encode_0 -> 0 [0] encode_s -> s [0] encode_gtr -> gtr [0] encode_d -> d [0] encode_len -> len [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [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(len, nil) -> 0 [1] app(c_app(d, x), 0) -> true [1] app(c_app(c_app(if, false), xs), ys) -> ys [1] app(c_app(gtr, 0), y) -> false [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) [1] app(c_app(filter, p), nil) -> nil [1] app(c_app(gtr, c_app(s, x)), 0) -> true [1] app(c_app(sub, x), 0) -> x [1] app(c_app(gtr, c_app(s, x)), c_app(s, y)) -> app(app(gtr, x), y) [1] app(c_app(sub, c_app(s, x)), c_app(s, y)) -> app(app(sub, x), y) [1] app(c_app(c_app(if, true), xs), ys) -> xs [1] app(len, c_app(c_app(cons, x), xs)) -> app(s, app(len, xs)) [1] app(c_app(filter, p), c_app(c_app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) [1] encArg(if) -> if [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(sub) -> sub [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(gtr) -> gtr [0] encArg(d) -> d [0] encArg(len) -> len [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [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_if -> if [0] encode_true -> true [0] encode_false -> false [0] encode_sub -> sub [0] encode_0 -> 0 [0] encode_s -> s [0] encode_gtr -> gtr [0] encode_d -> d [0] encode_len -> len [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] app(x0, x1) -> c_app(x0, x1) [0] The TRS has the following type information: app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app 0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app c_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encArg :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app cons_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app encode_filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons: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_if encode_true encode_false encode_sub encode_0 encode_s encode_gtr encode_d encode_len encode_nil encode_cons encode_filter app_2 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_if -> null_encode_if [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_sub -> null_encode_sub [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_gtr -> null_encode_gtr [0] encode_d -> null_encode_d [0] encode_len -> null_encode_len [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_if, null_encode_true, null_encode_false, null_encode_sub, null_encode_0, null_encode_s, null_encode_gtr, null_encode_d, null_encode_len, null_encode_nil, null_encode_cons, null_encode_filter, 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(len, nil) -> 0 [1] app(c_app(d, x), 0) -> true [1] app(c_app(c_app(if, false), xs), ys) -> ys [1] app(c_app(gtr, 0), y) -> false [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) [1] app(c_app(filter, p), nil) -> nil [1] app(c_app(gtr, c_app(s, x)), 0) -> true [1] app(c_app(sub, x), 0) -> x [1] app(c_app(gtr, c_app(s, x)), c_app(s, y)) -> app(app(gtr, x), y) [1] app(c_app(sub, c_app(s, x)), c_app(s, y)) -> app(app(sub, x), y) [1] app(c_app(c_app(if, true), xs), ys) -> xs [1] app(len, c_app(c_app(cons, x), xs)) -> app(s, app(len, xs)) [1] app(c_app(filter, p), c_app(c_app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) [1] encArg(if) -> if [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(sub) -> sub [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(gtr) -> gtr [0] encArg(d) -> d [0] encArg(len) -> len [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [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_if -> if [0] encode_true -> true [0] encode_false -> false [0] encode_sub -> sub [0] encode_0 -> 0 [0] encode_s -> s [0] encode_gtr -> gtr [0] encode_d -> d [0] encode_len -> len [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_if -> null_encode_if [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_sub -> null_encode_sub [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_gtr -> null_encode_gtr [0] encode_d -> null_encode_d [0] encode_len -> null_encode_len [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app 0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app c_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encArg :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app cons_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encArg :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter: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(len, nil) -> 0 [1] app(c_app(d, x), 0) -> true [1] app(c_app(c_app(if, false), xs), ys) -> ys [1] app(c_app(gtr, 0), y) -> false [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(c_app(gtr, x), y)), false), app(app(d, c_app(s, x)), app(c_app(sub, y), x))) [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(c_app(gtr, x), y)), false), app(app(d, c_app(s, x)), app(null_app, x))) [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(c_app(gtr, x), y)), false), app(app(d, null_app), app(c_app(sub, y), x))) [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(c_app(gtr, x), y)), false), app(app(d, null_app), app(null_app, x))) [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(null_app, y)), false), app(app(d, c_app(s, x)), app(c_app(sub, y), x))) [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(null_app, y)), false), app(app(d, c_app(s, x)), app(null_app, x))) [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(null_app, y)), false), app(app(d, null_app), app(c_app(sub, y), x))) [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(null_app, y)), false), app(app(d, null_app), app(null_app, x))) [1] app(c_app(filter, p), nil) -> nil [1] app(c_app(gtr, c_app(s, x)), 0) -> true [1] app(c_app(sub, x), 0) -> x [1] app(c_app(gtr, c_app(s, x)), c_app(s, y)) -> app(c_app(gtr, x), y) [1] app(c_app(gtr, c_app(s, x)), c_app(s, y)) -> app(null_app, y) [1] app(c_app(sub, c_app(s, x)), c_app(s, y)) -> app(c_app(sub, x), y) [1] app(c_app(sub, c_app(s, x)), c_app(s, y)) -> app(null_app, y) [1] app(c_app(c_app(if, true), xs), ys) -> xs [1] app(len, c_app(c_app(cons, x), nil)) -> app(s, 0) [2] app(len, c_app(c_app(cons, x), c_app(c_app(cons, x'), xs'))) -> app(s, app(s, app(len, xs'))) [2] app(len, c_app(c_app(cons, x), xs)) -> app(s, c_app(len, xs)) [1] app(len, c_app(c_app(cons, x), xs)) -> app(s, null_app) [1] app(c_app(filter, p), c_app(c_app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) [1] encArg(if) -> if [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(sub) -> sub [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(gtr) -> gtr [0] encArg(d) -> d [0] encArg(len) -> len [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [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_if -> if [0] encode_true -> true [0] encode_false -> false [0] encode_sub -> sub [0] encode_0 -> 0 [0] encode_s -> s [0] encode_gtr -> gtr [0] encode_d -> d [0] encode_len -> len [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_if -> null_encode_if [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_sub -> null_encode_sub [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_gtr -> null_encode_gtr [0] encode_d -> null_encode_d [0] encode_len -> null_encode_len [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app 0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app c_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encArg :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app cons_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encArg :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter: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: len => 7 nil => 8 0 => 0 d => 2 true => 11 if => 6 false => 3 gtr => 5 s => 9 sub => 10 filter => 4 cons => 1 null_encArg => 0 null_encode_app => 0 null_encode_if => 0 null_encode_true => 0 null_encode_false => 0 null_encode_sub => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_gtr => 0 null_encode_d => 0 null_encode_len => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_app => 0 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: app(z, z') -{ 1 }-> x :|: z = 1 + 10 + x, x >= 0, z' = 0 app(z, z') -{ 1 }-> xs :|: xs >= 0, z' = ys, ys >= 0, z = 1 + (1 + 6 + 11) + xs app(z, z') -{ 1 }-> ys :|: xs >= 0, z = 1 + (1 + 6 + 3) + xs, z' = ys, ys >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(p, x)), app(app(1, x), app(app(4, p), xs))), app(app(4, p), xs)) :|: xs >= 0, x >= 0, p >= 0, z = 1 + 4 + p, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(app(app(6, app(0, y)), 3), app(app(2, 0), app(0, x))) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 2 + (1 + 9 + x) app(z, z') -{ 1 }-> app(app(app(6, app(0, y)), 3), app(app(2, 0), app(1 + 10 + y, x))) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 2 + (1 + 9 + x) app(z, z') -{ 1 }-> app(app(app(6, app(0, y)), 3), app(app(2, 1 + 9 + x), app(0, x))) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 2 + (1 + 9 + x) app(z, z') -{ 1 }-> app(app(app(6, app(0, y)), 3), app(app(2, 1 + 9 + x), app(1 + 10 + y, x))) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 2 + (1 + 9 + x) app(z, z') -{ 1 }-> app(app(app(6, app(1 + 5 + x, y)), 3), app(app(2, 0), app(0, x))) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 2 + (1 + 9 + x) app(z, z') -{ 1 }-> app(app(app(6, app(1 + 5 + x, y)), 3), app(app(2, 0), app(1 + 10 + y, x))) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 2 + (1 + 9 + x) app(z, z') -{ 1 }-> app(app(app(6, app(1 + 5 + x, y)), 3), app(app(2, 1 + 9 + x), app(0, x))) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 2 + (1 + 9 + x) app(z, z') -{ 1 }-> app(app(app(6, app(1 + 5 + x, y)), 3), app(app(2, 1 + 9 + x), app(1 + 10 + y, x))) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 2 + (1 + 9 + x) app(z, z') -{ 2 }-> app(9, app(9, app(7, xs'))) :|: x >= 0, x' >= 0, xs' >= 0, z = 7, z' = 1 + (1 + 1 + x) + (1 + (1 + 1 + x') + xs') app(z, z') -{ 2 }-> app(9, 0) :|: x >= 0, z' = 1 + (1 + 1 + x) + 8, z = 7 app(z, z') -{ 1 }-> app(9, 0) :|: xs >= 0, x >= 0, z = 7, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(9, 1 + 7 + xs) :|: xs >= 0, x >= 0, z = 7, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(0, y) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 5 + (1 + 9 + x) app(z, z') -{ 1 }-> app(0, y) :|: z = 1 + 10 + (1 + 9 + x), z' = 1 + 9 + y, x >= 0, y >= 0 app(z, z') -{ 1 }-> app(1 + 5 + x, y) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 5 + (1 + 9 + x) app(z, z') -{ 1 }-> app(1 + 10 + x, y) :|: z = 1 + 10 + (1 + 9 + x), z' = 1 + 9 + y, x >= 0, y >= 0 app(z, z') -{ 1 }-> 8 :|: p >= 0, z' = 8, z = 1 + 4 + p app(z, z') -{ 1 }-> 3 :|: y >= 0, z = 1 + 5 + 0, z' = y app(z, z') -{ 1 }-> 11 :|: x >= 0, z = 1 + 2 + x, z' = 0 app(z, z') -{ 1 }-> 11 :|: x >= 0, z = 1 + 5 + (1 + 9 + x), z' = 0 app(z, z') -{ 1 }-> 0 :|: z' = 8, z = 7 app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 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 }-> 11 :|: z = 11 encArg(z) -{ 0 }-> 10 :|: z = 10 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_0 -{ 0 }-> 0 :|: encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_cons -{ 0 }-> 1 :|: encode_cons -{ 0 }-> 0 :|: encode_d -{ 0 }-> 2 :|: encode_d -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_gtr -{ 0 }-> 5 :|: encode_gtr -{ 0 }-> 0 :|: encode_if -{ 0 }-> 6 :|: encode_if -{ 0 }-> 0 :|: encode_len -{ 0 }-> 7 :|: encode_len -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 8 :|: encode_nil -{ 0 }-> 0 :|: encode_s -{ 0 }-> 9 :|: encode_s -{ 0 }-> 0 :|: encode_sub -{ 0 }-> 10 :|: encode_sub -{ 0 }-> 0 :|: encode_true -{ 0 }-> 11 :|: 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 - 11 >= 0, z' >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(0, z' - 10)), 3), app(app(2, 0), app(0, z - 13))) :|: z - 13 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(0, z' - 10)), 3), app(app(2, 0), app(1 + 10 + (z' - 10), z - 13))) :|: z - 13 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(0, z' - 10)), 3), app(app(2, 1 + 9 + (z - 13)), app(0, z - 13))) :|: z - 13 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(0, z' - 10)), 3), app(app(2, 1 + 9 + (z - 13)), app(1 + 10 + (z' - 10), z - 13))) :|: z - 13 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(z - 5, x)), app(app(1, x), app(app(4, z - 5), xs))), app(app(4, z - 5), xs)) :|: xs >= 0, x >= 0, z - 5 >= 0, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(app(app(6, app(1 + 5 + (z - 13), z' - 10)), 3), app(app(2, 0), app(0, z - 13))) :|: z - 13 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(1 + 5 + (z - 13), z' - 10)), 3), app(app(2, 0), app(1 + 10 + (z' - 10), z - 13))) :|: z - 13 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(1 + 5 + (z - 13), z' - 10)), 3), app(app(2, 1 + 9 + (z - 13)), app(0, z - 13))) :|: z - 13 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(1 + 5 + (z - 13), z' - 10)), 3), app(app(2, 1 + 9 + (z - 13)), app(1 + 10 + (z' - 10), z - 13))) :|: z - 13 >= 0, z' - 10 >= 0 app(z, z') -{ 2 }-> app(9, app(9, app(7, xs'))) :|: x >= 0, x' >= 0, xs' >= 0, z = 7, z' = 1 + (1 + 1 + x) + (1 + (1 + 1 + x') + xs') app(z, z') -{ 2 }-> app(9, 0) :|: z' - 11 >= 0, z = 7 app(z, z') -{ 1 }-> app(9, 0) :|: xs >= 0, x >= 0, z = 7, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(9, 1 + 7 + xs) :|: xs >= 0, x >= 0, z = 7, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(0, z' - 10) :|: z - 16 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(0, z' - 10) :|: z - 21 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(1 + 5 + (z - 16), z' - 10) :|: z - 16 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> app(1 + 10 + (z - 21), z' - 10) :|: z - 21 >= 0, z' - 10 >= 0 app(z, z') -{ 1 }-> 8 :|: z - 5 >= 0, z' = 8 app(z, z') -{ 1 }-> 3 :|: z' >= 0, z = 1 + 5 + 0 app(z, z') -{ 1 }-> 11 :|: z - 3 >= 0, z' = 0 app(z, z') -{ 1 }-> 11 :|: z - 16 >= 0, z' = 0 app(z, z') -{ 1 }-> 0 :|: z' = 8, z = 7 app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 app(z, z') -{ 1 }-> z - 19 :|: z - 19 >= 0, z' >= 0 app(z, z') -{ 1 }-> z - 11 :|: z - 11 >= 0, z' = 0 app(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 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 }-> 11 :|: z = 11 encArg(z) -{ 0 }-> 10 :|: z = 10 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encode_0 -{ 0 }-> 0 :|: encode_app(z, z') -{ 0 }-> app(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_cons -{ 0 }-> 1 :|: encode_cons -{ 0 }-> 0 :|: encode_d -{ 0 }-> 2 :|: encode_d -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_gtr -{ 0 }-> 5 :|: encode_gtr -{ 0 }-> 0 :|: encode_if -{ 0 }-> 6 :|: encode_if -{ 0 }-> 0 :|: encode_len -{ 0 }-> 7 :|: encode_len -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 8 :|: encode_nil -{ 0 }-> 0 :|: encode_s -{ 0 }-> 9 :|: encode_s -{ 0 }-> 0 :|: encode_sub -{ 0 }-> 10 :|: encode_sub -{ 0 }-> 0 :|: encode_true -{ 0 }-> 11 :|: 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_if -> null_encode_if [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_sub -> null_encode_sub [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_gtr -> null_encode_gtr [0] encode_d -> null_encode_d [0] encode_len -> null_encode_len [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_if, null_encode_true, null_encode_false, null_encode_sub, null_encode_0, null_encode_s, null_encode_gtr, null_encode_d, null_encode_len, null_encode_nil, null_encode_cons, null_encode_filter, 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(len, nil) -> 0 [1] app(c_app(d, x), 0) -> true [1] app(c_app(c_app(if, false), xs), ys) -> ys [1] app(c_app(gtr, 0), y) -> false [1] app(c_app(d, c_app(s, x)), c_app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x))) [1] app(c_app(filter, p), nil) -> nil [1] app(c_app(gtr, c_app(s, x)), 0) -> true [1] app(c_app(sub, x), 0) -> x [1] app(c_app(gtr, c_app(s, x)), c_app(s, y)) -> app(app(gtr, x), y) [1] app(c_app(sub, c_app(s, x)), c_app(s, y)) -> app(app(sub, x), y) [1] app(c_app(c_app(if, true), xs), ys) -> xs [1] app(len, c_app(c_app(cons, x), xs)) -> app(s, app(len, xs)) [1] app(c_app(filter, p), c_app(c_app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs)) [1] encArg(if) -> if [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(sub) -> sub [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(gtr) -> gtr [0] encArg(d) -> d [0] encArg(len) -> len [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [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_if -> if [0] encode_true -> true [0] encode_false -> false [0] encode_sub -> sub [0] encode_0 -> 0 [0] encode_s -> s [0] encode_gtr -> gtr [0] encode_d -> d [0] encode_len -> len [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_if -> null_encode_if [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_sub -> null_encode_sub [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_gtr -> null_encode_gtr [0] encode_d -> null_encode_d [0] encode_len -> null_encode_len [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app 0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app c_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encArg :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app cons_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app -> len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app encode_filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encArg :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_if :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_true :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_false :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_sub :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_0 :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_s :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_gtr :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_d :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_len :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_nil :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_cons :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_encode_filter :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter:null_app null_app :: len:nil:0:d:c_app:true:if:false:gtr:s:sub:filter:cons:cons_app:null_encArg:null_encode_app:null_encode_if:null_encode_true:null_encode_false:null_encode_sub:null_encode_0:null_encode_s:null_encode_gtr:null_encode_d:null_encode_len:null_encode_nil:null_encode_cons:null_encode_filter: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: len => 7 nil => 8 0 => 0 d => 2 true => 11 if => 6 false => 3 gtr => 5 s => 9 sub => 10 filter => 4 cons => 1 null_encArg => 0 null_encode_app => 0 null_encode_if => 0 null_encode_true => 0 null_encode_false => 0 null_encode_sub => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_gtr => 0 null_encode_d => 0 null_encode_len => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_app => 0 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: app(z, z') -{ 1 }-> x :|: z = 1 + 10 + x, x >= 0, z' = 0 app(z, z') -{ 1 }-> xs :|: xs >= 0, z' = ys, ys >= 0, z = 1 + (1 + 6 + 11) + xs app(z, z') -{ 1 }-> ys :|: xs >= 0, z = 1 + (1 + 6 + 3) + xs, z' = ys, ys >= 0 app(z, z') -{ 1 }-> app(app(app(6, app(p, x)), app(app(1, x), app(app(4, p), xs))), app(app(4, p), xs)) :|: xs >= 0, x >= 0, p >= 0, z = 1 + 4 + p, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(app(app(6, app(app(5, x), y)), 3), app(app(2, app(9, x)), app(app(10, y), x))) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 2 + (1 + 9 + x) app(z, z') -{ 1 }-> app(app(5, x), y) :|: z' = 1 + 9 + y, x >= 0, y >= 0, z = 1 + 5 + (1 + 9 + x) app(z, z') -{ 1 }-> app(app(10, x), y) :|: z = 1 + 10 + (1 + 9 + x), z' = 1 + 9 + y, x >= 0, y >= 0 app(z, z') -{ 1 }-> app(9, app(7, xs)) :|: xs >= 0, x >= 0, z = 7, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> 8 :|: p >= 0, z' = 8, z = 1 + 4 + p app(z, z') -{ 1 }-> 3 :|: y >= 0, z = 1 + 5 + 0, z' = y app(z, z') -{ 1 }-> 11 :|: x >= 0, z = 1 + 2 + x, z' = 0 app(z, z') -{ 1 }-> 11 :|: x >= 0, z = 1 + 5 + (1 + 9 + x), z' = 0 app(z, z') -{ 1 }-> 0 :|: z' = 8, z = 7 app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 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 }-> 11 :|: z = 11 encArg(z) -{ 0 }-> 10 :|: z = 10 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_0 -{ 0 }-> 0 :|: encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_cons -{ 0 }-> 1 :|: encode_cons -{ 0 }-> 0 :|: encode_d -{ 0 }-> 2 :|: encode_d -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_gtr -{ 0 }-> 5 :|: encode_gtr -{ 0 }-> 0 :|: encode_if -{ 0 }-> 6 :|: encode_if -{ 0 }-> 0 :|: encode_len -{ 0 }-> 7 :|: encode_len -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 8 :|: encode_nil -{ 0 }-> 0 :|: encode_s -{ 0 }-> 9 :|: encode_s -{ 0 }-> 0 :|: encode_sub -{ 0 }-> 10 :|: encode_sub -{ 0 }-> 0 :|: encode_true -{ 0 }-> 11 :|: 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(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: ENCARG(if) -> c ENCARG(true) -> c1 ENCARG(false) -> c2 ENCARG(sub) -> c3 ENCARG(0) -> c4 ENCARG(s) -> c5 ENCARG(gtr) -> c6 ENCARG(d) -> c7 ENCARG(len) -> c8 ENCARG(nil) -> c9 ENCARG(cons) -> c10 ENCARG(filter) -> c11 ENCARG(cons_app(z0, z1)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c13(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_IF -> c14 ENCODE_TRUE -> c15 ENCODE_FALSE -> c16 ENCODE_SUB -> c17 ENCODE_0 -> c18 ENCODE_S -> c19 ENCODE_GTR -> c20 ENCODE_D -> c21 ENCODE_LEN -> c22 ENCODE_NIL -> c23 ENCODE_CONS -> c24 ENCODE_FILTER -> c25 APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1), APP(sub, z0)) APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1), APP(gtr, z0)) APP(app(d, z0), 0) -> c33 APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(if, app(app(gtr, z0), z1)), false), APP(if, app(app(gtr, z0), z1)), APP(app(gtr, z0), z1), APP(gtr, z0), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(d, app(s, z0)), APP(s, z0), APP(app(sub, z1), z0), APP(sub, z1)) APP(len, nil) -> c35 APP(len, app(app(cons, z0), z1)) -> c36(APP(s, app(len, z1)), APP(len, z1)) APP(app(filter, z0), nil) -> c37 APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), APP(if, app(z0, z1)), APP(z0, z1), APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0), APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1), APP(sub, z0)) APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1), APP(gtr, z0)) APP(app(d, z0), 0) -> c33 APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(if, app(app(gtr, z0), z1)), false), APP(if, app(app(gtr, z0), z1)), APP(app(gtr, z0), z1), APP(gtr, z0), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(d, app(s, z0)), APP(s, z0), APP(app(sub, z1), z0), APP(sub, z1)) APP(len, nil) -> c35 APP(len, app(app(cons, z0), z1)) -> c36(APP(s, app(len, z1)), APP(len, z1)) APP(app(filter, z0), nil) -> c37 APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), APP(if, app(z0, z1)), APP(z0, z1), APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0), APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_if, encode_true, encode_false, encode_sub, encode_0, encode_s, encode_gtr, encode_d, encode_len, encode_nil, encode_cons, encode_filter Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, ENCODE_IF, ENCODE_TRUE, ENCODE_FALSE, ENCODE_SUB, ENCODE_0, ENCODE_S, ENCODE_GTR, ENCODE_D, ENCODE_LEN, ENCODE_NIL, ENCODE_CONS, ENCODE_FILTER, APP_2 Compound Symbols: c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12_3, c13_3, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29_2, c30, c31, c32_2, c33, c34_10, c35, c36_2, c37, c38_10 ---------------------------------------- (35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 24 trailing nodes: ENCARG(sub) -> c3 ENCARG(d) -> c7 ENCODE_NIL -> c23 ENCODE_S -> c19 ENCODE_0 -> c18 ENCARG(len) -> c8 ENCODE_D -> c21 ENCODE_FILTER -> c25 ENCARG(s) -> c5 ENCARG(0) -> c4 ENCARG(if) -> c ENCODE_IF -> c14 ENCODE_SUB -> c17 ENCODE_TRUE -> c15 ENCODE_GTR -> c20 ENCARG(true) -> c1 ENCODE_CONS -> c24 ENCARG(false) -> c2 ENCODE_FALSE -> c16 ENCARG(nil) -> c9 ENCARG(filter) -> c11 ENCARG(cons) -> c10 ENCODE_LEN -> c22 ENCARG(gtr) -> c6 ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c13(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1), APP(sub, z0)) APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1), APP(gtr, z0)) APP(app(d, z0), 0) -> c33 APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(if, app(app(gtr, z0), z1)), false), APP(if, app(app(gtr, z0), z1)), APP(app(gtr, z0), z1), APP(gtr, z0), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(d, app(s, z0)), APP(s, z0), APP(app(sub, z1), z0), APP(sub, z1)) APP(len, nil) -> c35 APP(len, app(app(cons, z0), z1)) -> c36(APP(s, app(len, z1)), APP(len, z1)) APP(app(filter, z0), nil) -> c37 APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), APP(if, app(z0, z1)), APP(z0, z1), APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0), APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1), APP(sub, z0)) APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1), APP(gtr, z0)) APP(app(d, z0), 0) -> c33 APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(if, app(app(gtr, z0), z1)), false), APP(if, app(app(gtr, z0), z1)), APP(app(gtr, z0), z1), APP(gtr, z0), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(d, app(s, z0)), APP(s, z0), APP(app(sub, z1), z0), APP(sub, z1)) APP(len, nil) -> c35 APP(len, app(app(cons, z0), z1)) -> c36(APP(s, app(len, z1)), APP(len, z1)) APP(app(filter, z0), nil) -> c37 APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), APP(if, app(z0, z1)), APP(z0, z1), APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0), APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_if, encode_true, encode_false, encode_sub, encode_0, encode_s, encode_gtr, encode_d, encode_len, encode_nil, encode_cons, encode_filter Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c12_3, c13_3, c26, c27, c28, c29_2, c30, c31, c32_2, c33, c34_10, c35, c36_2, c37, c38_10 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c13(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_if, encode_true, encode_false, encode_sub, encode_0, encode_s, encode_gtr, encode_d, encode_len, encode_nil, encode_cons, encode_filter Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c12_3, c13_3, c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c34_4, c36_1, c38_4 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), 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(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_if, encode_true, encode_false, encode_sub, encode_0, encode_s, encode_gtr, encode_d, encode_len, encode_nil, encode_cons, encode_filter Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c12_3, c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c34_4, c36_1, c38_4, 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(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_if, encode_true, encode_false, encode_sub, encode_0, encode_s, encode_gtr, encode_d, encode_len, encode_nil, encode_cons, encode_filter Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c12_3, c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c34_4, c36_1, c38_4, 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_if -> if encode_true -> true encode_false -> false encode_sub -> sub encode_0 -> 0 encode_s -> s encode_gtr -> gtr encode_d -> d encode_len -> len encode_nil -> nil encode_cons -> cons encode_filter -> filter ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), 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: c12_3, c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c34_4, c36_1, c38_4, c_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c12(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0), ENCARG(if)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0), ENCARG(sub)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0), ENCARG(gtr)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0), ENCARG(d)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0), ENCARG(len)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(if, x1)) -> c12(APP(if, encArg(x1)), ENCARG(if), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(APP(sub, encArg(x1)), ENCARG(sub), ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(APP(gtr, encArg(x1)), ENCARG(gtr), ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(APP(d, encArg(x1)), ENCARG(d), ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(len), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0), ENCARG(if)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0), ENCARG(sub)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0), ENCARG(gtr)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0), ENCARG(d)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0), ENCARG(len)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(if, x1)) -> c12(APP(if, encArg(x1)), ENCARG(if), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(APP(sub, encArg(x1)), ENCARG(sub), ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(APP(gtr, encArg(x1)), ENCARG(gtr), ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(APP(d, encArg(x1)), ENCARG(d), ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(len), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), 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: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c34_4, c36_1, c38_4, c_1, c12_3 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 35 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), 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: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c34_4, c36_1, c38_4, c_1, c12_3, c12_2, c12_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(d, app(s, z0)), app(s, z1)) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))), APP(app(gtr, z0), z1), APP(app(d, app(s, z0)), app(app(sub, z1), z0)), APP(app(sub, z1), z0)) by APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0)))), APP(app(gtr, app(s, z0)), 0), APP(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))), APP(app(sub, 0), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0)))), APP(app(gtr, app(s, z0)), 0), APP(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))), APP(app(sub, 0), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0)))), APP(app(gtr, app(s, z0)), 0), APP(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))), APP(app(sub, 0), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c38_4, c_1, c12_3, c12_2, c12_1, c34_4 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0)))), APP(app(gtr, app(s, z0)), 0)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0)))), APP(app(gtr, app(s, z0)), 0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c38_4, c_1, c12_3, c12_2, c12_1, c34_4, c34_2 ---------------------------------------- (53) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c38_4, c_1, c12_3, c12_2, c12_1, c34_4, c1_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c38(APP(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)), APP(z0, z1), APP(app(filter, z0), z2), APP(app(filter, z0), z2)) by APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x2))), app(app(filter, len), x2)), APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x2))), app(app(filter, len), x2)), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x2))), app(app(filter, len), x2)), APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x2))), app(app(filter, len), x2)), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x2))), app(app(filter, len), x2)), APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x2))), app(app(filter, len), x2)), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c_1, c12_3, c12_2, c12_1, c34_4, c1_1, c38_4 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c_1, c12_3, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(if, x1) -> c(APP(if, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(sub, x1) -> c(APP(sub, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(s, x1) -> c(APP(s, encArg(x1))) ENCODE_APP(gtr, x1) -> c(APP(gtr, encArg(x1))) ENCODE_APP(d, x1) -> c(APP(d, encArg(x1))) ENCODE_APP(len, x1) -> c(APP(len, 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(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(if, x1) -> c(APP(if, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(sub, x1) -> c(APP(sub, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(s, x1) -> c(APP(s, encArg(x1))) ENCODE_APP(gtr, x1) -> c(APP(gtr, encArg(x1))) ENCODE_APP(d, x1) -> c(APP(d, encArg(x1))) ENCODE_APP(len, x1) -> c(APP(len, 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(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_3, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1 ---------------------------------------- (61) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 11 trailing nodes: ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(s, x1) -> c(APP(s, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(d, x1) -> c(APP(d, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(gtr, x1) -> c(APP(gtr, encArg(x1))) ENCODE_APP(sub, x1) -> c(APP(sub, encArg(x1))) ENCODE_APP(if, x1) -> c(APP(if, encArg(x1))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_3, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c12(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by ENCARG(cons_app(x0, cons_app(x1, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(APP(if, app(encArg(x1), encArg(x2))), ENCARG(if), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(APP(sub, app(encArg(x1), encArg(x2))), ENCARG(sub), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(APP(gtr, app(encArg(x1), encArg(x2))), ENCARG(gtr), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(APP(d, app(encArg(x1), encArg(x2))), ENCARG(d), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(len), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(APP(if, app(encArg(x1), encArg(x2))), ENCARG(if), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(APP(sub, app(encArg(x1), encArg(x2))), ENCARG(sub), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(APP(gtr, app(encArg(x1), encArg(x2))), ENCARG(gtr), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(APP(d, app(encArg(x1), encArg(x2))), ENCARG(d), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(len), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c12(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(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_3, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 23 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_3, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c12(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by ENCARG(cons_app(cons_app(x0, x1), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1)), ENCARG(if)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1)), ENCARG(sub)) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0)) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s)) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1)), ENCARG(gtr)) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1)), ENCARG(d)) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1)), ENCARG(len)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c12(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, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(if, x1), x2)) -> c12(APP(app(if, encArg(x1)), encArg(x2)), ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1)), ENCARG(if)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1)), ENCARG(sub)) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0)) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s)) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1)), ENCARG(gtr)) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1)), ENCARG(d)) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1)), ENCARG(len)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(if, x1), x2)) -> c12(APP(app(if, encArg(x1)), encArg(x2)), ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 19 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, if)) -> c12(APP(encArg(x0), if), ENCARG(x0)) by ENCARG(cons_app(if, if)) -> c12(APP(if, if), ENCARG(if)) ENCARG(cons_app(true, if)) -> c12(APP(true, if), ENCARG(true)) ENCARG(cons_app(false, if)) -> c12(APP(false, if), ENCARG(false)) ENCARG(cons_app(sub, if)) -> c12(APP(sub, if), ENCARG(sub)) ENCARG(cons_app(0, if)) -> c12(APP(0, if), ENCARG(0)) ENCARG(cons_app(s, if)) -> c12(APP(s, if), ENCARG(s)) ENCARG(cons_app(gtr, if)) -> c12(APP(gtr, if), ENCARG(gtr)) ENCARG(cons_app(d, if)) -> c12(APP(d, if), ENCARG(d)) ENCARG(cons_app(len, if)) -> c12(APP(len, if), ENCARG(len)) ENCARG(cons_app(nil, if)) -> c12(APP(nil, if), ENCARG(nil)) ENCARG(cons_app(cons, if)) -> c12(APP(cons, if), ENCARG(cons)) ENCARG(cons_app(filter, if)) -> c12(APP(filter, if), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), if)) -> c12(APP(app(encArg(z0), encArg(z1)), if), ENCARG(cons_app(z0, z1))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, if)) -> c12(APP(if, if), ENCARG(if)) ENCARG(cons_app(true, if)) -> c12(APP(true, if), ENCARG(true)) ENCARG(cons_app(false, if)) -> c12(APP(false, if), ENCARG(false)) ENCARG(cons_app(sub, if)) -> c12(APP(sub, if), ENCARG(sub)) ENCARG(cons_app(0, if)) -> c12(APP(0, if), ENCARG(0)) ENCARG(cons_app(s, if)) -> c12(APP(s, if), ENCARG(s)) ENCARG(cons_app(gtr, if)) -> c12(APP(gtr, if), ENCARG(gtr)) ENCARG(cons_app(d, if)) -> c12(APP(d, if), ENCARG(d)) ENCARG(cons_app(len, if)) -> c12(APP(len, if), ENCARG(len)) ENCARG(cons_app(nil, if)) -> c12(APP(nil, if), ENCARG(nil)) ENCARG(cons_app(cons, if)) -> c12(APP(cons, if), ENCARG(cons)) ENCARG(cons_app(filter, if)) -> c12(APP(filter, if), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(gtr, if)) -> c12(APP(gtr, if), ENCARG(gtr)) ENCARG(cons_app(cons, if)) -> c12(APP(cons, if), ENCARG(cons)) ENCARG(cons_app(s, if)) -> c12(APP(s, if), ENCARG(s)) ENCARG(cons_app(false, if)) -> c12(APP(false, if), ENCARG(false)) ENCARG(cons_app(len, if)) -> c12(APP(len, if), ENCARG(len)) ENCARG(cons_app(0, if)) -> c12(APP(0, if), ENCARG(0)) ENCARG(cons_app(true, if)) -> c12(APP(true, if), ENCARG(true)) ENCARG(cons_app(if, if)) -> c12(APP(if, if), ENCARG(if)) ENCARG(cons_app(nil, if)) -> c12(APP(nil, if), ENCARG(nil)) ENCARG(cons_app(d, if)) -> c12(APP(d, if), ENCARG(d)) ENCARG(cons_app(sub, if)) -> c12(APP(sub, if), ENCARG(sub)) ENCARG(cons_app(filter, if)) -> c12(APP(filter, if), ENCARG(filter)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, true)) -> c12(APP(encArg(x0), true), ENCARG(x0)) by ENCARG(cons_app(if, true)) -> c12(APP(if, true), ENCARG(if)) ENCARG(cons_app(true, true)) -> c12(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c12(APP(false, true), ENCARG(false)) ENCARG(cons_app(sub, true)) -> c12(APP(sub, true), ENCARG(sub)) ENCARG(cons_app(0, true)) -> c12(APP(0, true), ENCARG(0)) ENCARG(cons_app(s, true)) -> c12(APP(s, true), ENCARG(s)) ENCARG(cons_app(gtr, true)) -> c12(APP(gtr, true), ENCARG(gtr)) ENCARG(cons_app(d, true)) -> c12(APP(d, true), ENCARG(d)) ENCARG(cons_app(len, true)) -> c12(APP(len, true), ENCARG(len)) ENCARG(cons_app(nil, true)) -> c12(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c12(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(filter, true)) -> c12(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), true)) -> c12(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, true)) -> c12(APP(if, true), ENCARG(if)) ENCARG(cons_app(true, true)) -> c12(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c12(APP(false, true), ENCARG(false)) ENCARG(cons_app(sub, true)) -> c12(APP(sub, true), ENCARG(sub)) ENCARG(cons_app(0, true)) -> c12(APP(0, true), ENCARG(0)) ENCARG(cons_app(s, true)) -> c12(APP(s, true), ENCARG(s)) ENCARG(cons_app(gtr, true)) -> c12(APP(gtr, true), ENCARG(gtr)) ENCARG(cons_app(d, true)) -> c12(APP(d, true), ENCARG(d)) ENCARG(cons_app(len, true)) -> c12(APP(len, true), ENCARG(len)) ENCARG(cons_app(nil, true)) -> c12(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c12(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(filter, true)) -> c12(APP(filter, true), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(filter, true)) -> c12(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(len, true)) -> c12(APP(len, true), ENCARG(len)) ENCARG(cons_app(0, true)) -> c12(APP(0, true), ENCARG(0)) ENCARG(cons_app(if, true)) -> c12(APP(if, true), ENCARG(if)) ENCARG(cons_app(cons, true)) -> c12(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(d, true)) -> c12(APP(d, true), ENCARG(d)) ENCARG(cons_app(sub, true)) -> c12(APP(sub, true), ENCARG(sub)) ENCARG(cons_app(s, true)) -> c12(APP(s, true), ENCARG(s)) ENCARG(cons_app(false, true)) -> c12(APP(false, true), ENCARG(false)) ENCARG(cons_app(true, true)) -> c12(APP(true, true), ENCARG(true)) ENCARG(cons_app(nil, true)) -> c12(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(gtr, true)) -> c12(APP(gtr, true), ENCARG(gtr)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, false)) -> c12(APP(encArg(x0), false), ENCARG(x0)) by ENCARG(cons_app(if, false)) -> c12(APP(if, false), ENCARG(if)) ENCARG(cons_app(true, false)) -> c12(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c12(APP(false, false), ENCARG(false)) ENCARG(cons_app(sub, false)) -> c12(APP(sub, false), ENCARG(sub)) ENCARG(cons_app(0, false)) -> c12(APP(0, false), ENCARG(0)) ENCARG(cons_app(s, false)) -> c12(APP(s, false), ENCARG(s)) ENCARG(cons_app(gtr, false)) -> c12(APP(gtr, false), ENCARG(gtr)) ENCARG(cons_app(d, false)) -> c12(APP(d, false), ENCARG(d)) ENCARG(cons_app(len, false)) -> c12(APP(len, false), ENCARG(len)) ENCARG(cons_app(nil, false)) -> c12(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c12(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(filter, false)) -> c12(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), false)) -> c12(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, false)) -> c12(APP(if, false), ENCARG(if)) ENCARG(cons_app(true, false)) -> c12(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c12(APP(false, false), ENCARG(false)) ENCARG(cons_app(sub, false)) -> c12(APP(sub, false), ENCARG(sub)) ENCARG(cons_app(0, false)) -> c12(APP(0, false), ENCARG(0)) ENCARG(cons_app(s, false)) -> c12(APP(s, false), ENCARG(s)) ENCARG(cons_app(gtr, false)) -> c12(APP(gtr, false), ENCARG(gtr)) ENCARG(cons_app(d, false)) -> c12(APP(d, false), ENCARG(d)) ENCARG(cons_app(len, false)) -> c12(APP(len, false), ENCARG(len)) ENCARG(cons_app(nil, false)) -> c12(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c12(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(filter, false)) -> c12(APP(filter, false), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(cons, false)) -> c12(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(d, false)) -> c12(APP(d, false), ENCARG(d)) ENCARG(cons_app(sub, false)) -> c12(APP(sub, false), ENCARG(sub)) ENCARG(cons_app(len, false)) -> c12(APP(len, false), ENCARG(len)) ENCARG(cons_app(s, false)) -> c12(APP(s, false), ENCARG(s)) ENCARG(cons_app(false, false)) -> c12(APP(false, false), ENCARG(false)) ENCARG(cons_app(nil, false)) -> c12(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(true, false)) -> c12(APP(true, false), ENCARG(true)) ENCARG(cons_app(0, false)) -> c12(APP(0, false), ENCARG(0)) ENCARG(cons_app(if, false)) -> c12(APP(if, false), ENCARG(if)) ENCARG(cons_app(gtr, false)) -> c12(APP(gtr, false), ENCARG(gtr)) ENCARG(cons_app(filter, false)) -> c12(APP(filter, false), ENCARG(filter)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, sub)) -> c12(APP(encArg(x0), sub), ENCARG(x0)) by ENCARG(cons_app(if, sub)) -> c12(APP(if, sub), ENCARG(if)) ENCARG(cons_app(true, sub)) -> c12(APP(true, sub), ENCARG(true)) ENCARG(cons_app(false, sub)) -> c12(APP(false, sub), ENCARG(false)) ENCARG(cons_app(sub, sub)) -> c12(APP(sub, sub), ENCARG(sub)) ENCARG(cons_app(0, sub)) -> c12(APP(0, sub), ENCARG(0)) ENCARG(cons_app(s, sub)) -> c12(APP(s, sub), ENCARG(s)) ENCARG(cons_app(gtr, sub)) -> c12(APP(gtr, sub), ENCARG(gtr)) ENCARG(cons_app(d, sub)) -> c12(APP(d, sub), ENCARG(d)) ENCARG(cons_app(len, sub)) -> c12(APP(len, sub), ENCARG(len)) ENCARG(cons_app(nil, sub)) -> c12(APP(nil, sub), ENCARG(nil)) ENCARG(cons_app(cons, sub)) -> c12(APP(cons, sub), ENCARG(cons)) ENCARG(cons_app(filter, sub)) -> c12(APP(filter, sub), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), sub)) -> c12(APP(app(encArg(z0), encArg(z1)), sub), ENCARG(cons_app(z0, z1))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, sub)) -> c12(APP(if, sub), ENCARG(if)) ENCARG(cons_app(true, sub)) -> c12(APP(true, sub), ENCARG(true)) ENCARG(cons_app(false, sub)) -> c12(APP(false, sub), ENCARG(false)) ENCARG(cons_app(sub, sub)) -> c12(APP(sub, sub), ENCARG(sub)) ENCARG(cons_app(0, sub)) -> c12(APP(0, sub), ENCARG(0)) ENCARG(cons_app(s, sub)) -> c12(APP(s, sub), ENCARG(s)) ENCARG(cons_app(gtr, sub)) -> c12(APP(gtr, sub), ENCARG(gtr)) ENCARG(cons_app(d, sub)) -> c12(APP(d, sub), ENCARG(d)) ENCARG(cons_app(len, sub)) -> c12(APP(len, sub), ENCARG(len)) ENCARG(cons_app(nil, sub)) -> c12(APP(nil, sub), ENCARG(nil)) ENCARG(cons_app(cons, sub)) -> c12(APP(cons, sub), ENCARG(cons)) ENCARG(cons_app(filter, sub)) -> c12(APP(filter, sub), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(d, sub)) -> c12(APP(d, sub), ENCARG(d)) ENCARG(cons_app(s, sub)) -> c12(APP(s, sub), ENCARG(s)) ENCARG(cons_app(sub, sub)) -> c12(APP(sub, sub), ENCARG(sub)) ENCARG(cons_app(filter, sub)) -> c12(APP(filter, sub), ENCARG(filter)) ENCARG(cons_app(cons, sub)) -> c12(APP(cons, sub), ENCARG(cons)) ENCARG(cons_app(gtr, sub)) -> c12(APP(gtr, sub), ENCARG(gtr)) ENCARG(cons_app(false, sub)) -> c12(APP(false, sub), ENCARG(false)) ENCARG(cons_app(true, sub)) -> c12(APP(true, sub), ENCARG(true)) ENCARG(cons_app(nil, sub)) -> c12(APP(nil, sub), ENCARG(nil)) ENCARG(cons_app(0, sub)) -> c12(APP(0, sub), ENCARG(0)) ENCARG(cons_app(if, sub)) -> c12(APP(if, sub), ENCARG(if)) ENCARG(cons_app(len, sub)) -> c12(APP(len, sub), ENCARG(len)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, 0)) -> c12(APP(encArg(x0), 0), ENCARG(x0)) by ENCARG(cons_app(if, 0)) -> c12(APP(if, 0), ENCARG(if)) ENCARG(cons_app(true, 0)) -> c12(APP(true, 0), ENCARG(true)) ENCARG(cons_app(false, 0)) -> c12(APP(false, 0), ENCARG(false)) ENCARG(cons_app(sub, 0)) -> c12(APP(sub, 0), ENCARG(sub)) ENCARG(cons_app(0, 0)) -> c12(APP(0, 0), ENCARG(0)) ENCARG(cons_app(s, 0)) -> c12(APP(s, 0), ENCARG(s)) ENCARG(cons_app(gtr, 0)) -> c12(APP(gtr, 0), ENCARG(gtr)) ENCARG(cons_app(d, 0)) -> c12(APP(d, 0), ENCARG(d)) ENCARG(cons_app(len, 0)) -> c12(APP(len, 0), ENCARG(len)) ENCARG(cons_app(nil, 0)) -> c12(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(cons, 0)) -> c12(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(filter, 0)) -> c12(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), 0)) -> c12(APP(app(encArg(z0), encArg(z1)), 0), ENCARG(cons_app(z0, z1))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, 0)) -> c12(APP(if, 0), ENCARG(if)) ENCARG(cons_app(true, 0)) -> c12(APP(true, 0), ENCARG(true)) ENCARG(cons_app(false, 0)) -> c12(APP(false, 0), ENCARG(false)) ENCARG(cons_app(sub, 0)) -> c12(APP(sub, 0), ENCARG(sub)) ENCARG(cons_app(0, 0)) -> c12(APP(0, 0), ENCARG(0)) ENCARG(cons_app(s, 0)) -> c12(APP(s, 0), ENCARG(s)) ENCARG(cons_app(gtr, 0)) -> c12(APP(gtr, 0), ENCARG(gtr)) ENCARG(cons_app(d, 0)) -> c12(APP(d, 0), ENCARG(d)) ENCARG(cons_app(len, 0)) -> c12(APP(len, 0), ENCARG(len)) ENCARG(cons_app(nil, 0)) -> c12(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(cons, 0)) -> c12(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(filter, 0)) -> c12(APP(filter, 0), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(s, 0)) -> c12(APP(s, 0), ENCARG(s)) ENCARG(cons_app(false, 0)) -> c12(APP(false, 0), ENCARG(false)) ENCARG(cons_app(nil, 0)) -> c12(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(len, 0)) -> c12(APP(len, 0), ENCARG(len)) ENCARG(cons_app(d, 0)) -> c12(APP(d, 0), ENCARG(d)) ENCARG(cons_app(sub, 0)) -> c12(APP(sub, 0), ENCARG(sub)) ENCARG(cons_app(filter, 0)) -> c12(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(if, 0)) -> c12(APP(if, 0), ENCARG(if)) ENCARG(cons_app(cons, 0)) -> c12(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(true, 0)) -> c12(APP(true, 0), ENCARG(true)) ENCARG(cons_app(gtr, 0)) -> c12(APP(gtr, 0), ENCARG(gtr)) ENCARG(cons_app(0, 0)) -> c12(APP(0, 0), ENCARG(0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, s)) -> c12(APP(encArg(x0), s), ENCARG(x0)) by ENCARG(cons_app(if, s)) -> c12(APP(if, s), ENCARG(if)) ENCARG(cons_app(true, s)) -> c12(APP(true, s), ENCARG(true)) ENCARG(cons_app(false, s)) -> c12(APP(false, s), ENCARG(false)) ENCARG(cons_app(sub, s)) -> c12(APP(sub, s), ENCARG(sub)) ENCARG(cons_app(0, s)) -> c12(APP(0, s), ENCARG(0)) ENCARG(cons_app(s, s)) -> c12(APP(s, s), ENCARG(s)) ENCARG(cons_app(gtr, s)) -> c12(APP(gtr, s), ENCARG(gtr)) ENCARG(cons_app(d, s)) -> c12(APP(d, s), ENCARG(d)) ENCARG(cons_app(len, s)) -> c12(APP(len, s), ENCARG(len)) ENCARG(cons_app(nil, s)) -> c12(APP(nil, s), ENCARG(nil)) ENCARG(cons_app(cons, s)) -> c12(APP(cons, s), ENCARG(cons)) ENCARG(cons_app(filter, s)) -> c12(APP(filter, s), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), s)) -> c12(APP(app(encArg(z0), encArg(z1)), s), ENCARG(cons_app(z0, z1))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, s)) -> c12(APP(if, s), ENCARG(if)) ENCARG(cons_app(true, s)) -> c12(APP(true, s), ENCARG(true)) ENCARG(cons_app(false, s)) -> c12(APP(false, s), ENCARG(false)) ENCARG(cons_app(sub, s)) -> c12(APP(sub, s), ENCARG(sub)) ENCARG(cons_app(0, s)) -> c12(APP(0, s), ENCARG(0)) ENCARG(cons_app(s, s)) -> c12(APP(s, s), ENCARG(s)) ENCARG(cons_app(gtr, s)) -> c12(APP(gtr, s), ENCARG(gtr)) ENCARG(cons_app(d, s)) -> c12(APP(d, s), ENCARG(d)) ENCARG(cons_app(len, s)) -> c12(APP(len, s), ENCARG(len)) ENCARG(cons_app(nil, s)) -> c12(APP(nil, s), ENCARG(nil)) ENCARG(cons_app(cons, s)) -> c12(APP(cons, s), ENCARG(cons)) ENCARG(cons_app(filter, s)) -> c12(APP(filter, s), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(filter, s)) -> c12(APP(filter, s), ENCARG(filter)) ENCARG(cons_app(nil, s)) -> c12(APP(nil, s), ENCARG(nil)) ENCARG(cons_app(false, s)) -> c12(APP(false, s), ENCARG(false)) ENCARG(cons_app(d, s)) -> c12(APP(d, s), ENCARG(d)) ENCARG(cons_app(sub, s)) -> c12(APP(sub, s), ENCARG(sub)) ENCARG(cons_app(true, s)) -> c12(APP(true, s), ENCARG(true)) ENCARG(cons_app(len, s)) -> c12(APP(len, s), ENCARG(len)) ENCARG(cons_app(s, s)) -> c12(APP(s, s), ENCARG(s)) ENCARG(cons_app(if, s)) -> c12(APP(if, s), ENCARG(if)) ENCARG(cons_app(0, s)) -> c12(APP(0, s), ENCARG(0)) ENCARG(cons_app(gtr, s)) -> c12(APP(gtr, s), ENCARG(gtr)) ENCARG(cons_app(cons, s)) -> c12(APP(cons, s), ENCARG(cons)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, gtr)) -> c12(APP(encArg(x0), gtr), ENCARG(x0)) by ENCARG(cons_app(if, gtr)) -> c12(APP(if, gtr), ENCARG(if)) ENCARG(cons_app(true, gtr)) -> c12(APP(true, gtr), ENCARG(true)) ENCARG(cons_app(false, gtr)) -> c12(APP(false, gtr), ENCARG(false)) ENCARG(cons_app(sub, gtr)) -> c12(APP(sub, gtr), ENCARG(sub)) ENCARG(cons_app(0, gtr)) -> c12(APP(0, gtr), ENCARG(0)) ENCARG(cons_app(s, gtr)) -> c12(APP(s, gtr), ENCARG(s)) ENCARG(cons_app(gtr, gtr)) -> c12(APP(gtr, gtr), ENCARG(gtr)) ENCARG(cons_app(d, gtr)) -> c12(APP(d, gtr), ENCARG(d)) ENCARG(cons_app(len, gtr)) -> c12(APP(len, gtr), ENCARG(len)) ENCARG(cons_app(nil, gtr)) -> c12(APP(nil, gtr), ENCARG(nil)) ENCARG(cons_app(cons, gtr)) -> c12(APP(cons, gtr), ENCARG(cons)) ENCARG(cons_app(filter, gtr)) -> c12(APP(filter, gtr), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), gtr)) -> c12(APP(app(encArg(z0), encArg(z1)), gtr), ENCARG(cons_app(z0, z1))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, gtr)) -> c12(APP(if, gtr), ENCARG(if)) ENCARG(cons_app(true, gtr)) -> c12(APP(true, gtr), ENCARG(true)) ENCARG(cons_app(false, gtr)) -> c12(APP(false, gtr), ENCARG(false)) ENCARG(cons_app(sub, gtr)) -> c12(APP(sub, gtr), ENCARG(sub)) ENCARG(cons_app(0, gtr)) -> c12(APP(0, gtr), ENCARG(0)) ENCARG(cons_app(s, gtr)) -> c12(APP(s, gtr), ENCARG(s)) ENCARG(cons_app(gtr, gtr)) -> c12(APP(gtr, gtr), ENCARG(gtr)) ENCARG(cons_app(d, gtr)) -> c12(APP(d, gtr), ENCARG(d)) ENCARG(cons_app(len, gtr)) -> c12(APP(len, gtr), ENCARG(len)) ENCARG(cons_app(nil, gtr)) -> c12(APP(nil, gtr), ENCARG(nil)) ENCARG(cons_app(cons, gtr)) -> c12(APP(cons, gtr), ENCARG(cons)) ENCARG(cons_app(filter, gtr)) -> c12(APP(filter, gtr), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(if, gtr)) -> c12(APP(if, gtr), ENCARG(if)) ENCARG(cons_app(filter, gtr)) -> c12(APP(filter, gtr), ENCARG(filter)) ENCARG(cons_app(cons, gtr)) -> c12(APP(cons, gtr), ENCARG(cons)) ENCARG(cons_app(len, gtr)) -> c12(APP(len, gtr), ENCARG(len)) ENCARG(cons_app(false, gtr)) -> c12(APP(false, gtr), ENCARG(false)) ENCARG(cons_app(true, gtr)) -> c12(APP(true, gtr), ENCARG(true)) ENCARG(cons_app(gtr, gtr)) -> c12(APP(gtr, gtr), ENCARG(gtr)) ENCARG(cons_app(s, gtr)) -> c12(APP(s, gtr), ENCARG(s)) ENCARG(cons_app(nil, gtr)) -> c12(APP(nil, gtr), ENCARG(nil)) ENCARG(cons_app(d, gtr)) -> c12(APP(d, gtr), ENCARG(d)) ENCARG(cons_app(0, gtr)) -> c12(APP(0, gtr), ENCARG(0)) ENCARG(cons_app(sub, gtr)) -> c12(APP(sub, gtr), ENCARG(sub)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, d)) -> c12(APP(encArg(x0), d), ENCARG(x0)) by ENCARG(cons_app(if, d)) -> c12(APP(if, d), ENCARG(if)) ENCARG(cons_app(true, d)) -> c12(APP(true, d), ENCARG(true)) ENCARG(cons_app(false, d)) -> c12(APP(false, d), ENCARG(false)) ENCARG(cons_app(sub, d)) -> c12(APP(sub, d), ENCARG(sub)) ENCARG(cons_app(0, d)) -> c12(APP(0, d), ENCARG(0)) ENCARG(cons_app(s, d)) -> c12(APP(s, d), ENCARG(s)) ENCARG(cons_app(gtr, d)) -> c12(APP(gtr, d), ENCARG(gtr)) ENCARG(cons_app(d, d)) -> c12(APP(d, d), ENCARG(d)) ENCARG(cons_app(len, d)) -> c12(APP(len, d), ENCARG(len)) ENCARG(cons_app(nil, d)) -> c12(APP(nil, d), ENCARG(nil)) ENCARG(cons_app(cons, d)) -> c12(APP(cons, d), ENCARG(cons)) ENCARG(cons_app(filter, d)) -> c12(APP(filter, d), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), d)) -> c12(APP(app(encArg(z0), encArg(z1)), d), ENCARG(cons_app(z0, z1))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, d)) -> c12(APP(if, d), ENCARG(if)) ENCARG(cons_app(true, d)) -> c12(APP(true, d), ENCARG(true)) ENCARG(cons_app(false, d)) -> c12(APP(false, d), ENCARG(false)) ENCARG(cons_app(sub, d)) -> c12(APP(sub, d), ENCARG(sub)) ENCARG(cons_app(0, d)) -> c12(APP(0, d), ENCARG(0)) ENCARG(cons_app(s, d)) -> c12(APP(s, d), ENCARG(s)) ENCARG(cons_app(gtr, d)) -> c12(APP(gtr, d), ENCARG(gtr)) ENCARG(cons_app(d, d)) -> c12(APP(d, d), ENCARG(d)) ENCARG(cons_app(len, d)) -> c12(APP(len, d), ENCARG(len)) ENCARG(cons_app(nil, d)) -> c12(APP(nil, d), ENCARG(nil)) ENCARG(cons_app(cons, d)) -> c12(APP(cons, d), ENCARG(cons)) ENCARG(cons_app(filter, d)) -> c12(APP(filter, d), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(d, d)) -> c12(APP(d, d), ENCARG(d)) ENCARG(cons_app(sub, d)) -> c12(APP(sub, d), ENCARG(sub)) ENCARG(cons_app(nil, d)) -> c12(APP(nil, d), ENCARG(nil)) ENCARG(cons_app(gtr, d)) -> c12(APP(gtr, d), ENCARG(gtr)) ENCARG(cons_app(if, d)) -> c12(APP(if, d), ENCARG(if)) ENCARG(cons_app(len, d)) -> c12(APP(len, d), ENCARG(len)) ENCARG(cons_app(true, d)) -> c12(APP(true, d), ENCARG(true)) ENCARG(cons_app(cons, d)) -> c12(APP(cons, d), ENCARG(cons)) ENCARG(cons_app(filter, d)) -> c12(APP(filter, d), ENCARG(filter)) ENCARG(cons_app(false, d)) -> c12(APP(false, d), ENCARG(false)) ENCARG(cons_app(0, d)) -> c12(APP(0, d), ENCARG(0)) ENCARG(cons_app(s, d)) -> c12(APP(s, d), ENCARG(s)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, len)) -> c12(APP(encArg(x0), len), ENCARG(x0)) by ENCARG(cons_app(if, len)) -> c12(APP(if, len), ENCARG(if)) ENCARG(cons_app(true, len)) -> c12(APP(true, len), ENCARG(true)) ENCARG(cons_app(false, len)) -> c12(APP(false, len), ENCARG(false)) ENCARG(cons_app(sub, len)) -> c12(APP(sub, len), ENCARG(sub)) ENCARG(cons_app(0, len)) -> c12(APP(0, len), ENCARG(0)) ENCARG(cons_app(s, len)) -> c12(APP(s, len), ENCARG(s)) ENCARG(cons_app(gtr, len)) -> c12(APP(gtr, len), ENCARG(gtr)) ENCARG(cons_app(d, len)) -> c12(APP(d, len), ENCARG(d)) ENCARG(cons_app(len, len)) -> c12(APP(len, len), ENCARG(len)) ENCARG(cons_app(nil, len)) -> c12(APP(nil, len), ENCARG(nil)) ENCARG(cons_app(cons, len)) -> c12(APP(cons, len), ENCARG(cons)) ENCARG(cons_app(filter, len)) -> c12(APP(filter, len), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), len)) -> c12(APP(app(encArg(z0), encArg(z1)), len), ENCARG(cons_app(z0, z1))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, len)) -> c12(APP(if, len), ENCARG(if)) ENCARG(cons_app(true, len)) -> c12(APP(true, len), ENCARG(true)) ENCARG(cons_app(false, len)) -> c12(APP(false, len), ENCARG(false)) ENCARG(cons_app(sub, len)) -> c12(APP(sub, len), ENCARG(sub)) ENCARG(cons_app(0, len)) -> c12(APP(0, len), ENCARG(0)) ENCARG(cons_app(s, len)) -> c12(APP(s, len), ENCARG(s)) ENCARG(cons_app(gtr, len)) -> c12(APP(gtr, len), ENCARG(gtr)) ENCARG(cons_app(d, len)) -> c12(APP(d, len), ENCARG(d)) ENCARG(cons_app(len, len)) -> c12(APP(len, len), ENCARG(len)) ENCARG(cons_app(nil, len)) -> c12(APP(nil, len), ENCARG(nil)) ENCARG(cons_app(cons, len)) -> c12(APP(cons, len), ENCARG(cons)) ENCARG(cons_app(filter, len)) -> c12(APP(filter, len), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(0, len)) -> c12(APP(0, len), ENCARG(0)) ENCARG(cons_app(d, len)) -> c12(APP(d, len), ENCARG(d)) ENCARG(cons_app(sub, len)) -> c12(APP(sub, len), ENCARG(sub)) ENCARG(cons_app(gtr, len)) -> c12(APP(gtr, len), ENCARG(gtr)) ENCARG(cons_app(true, len)) -> c12(APP(true, len), ENCARG(true)) ENCARG(cons_app(nil, len)) -> c12(APP(nil, len), ENCARG(nil)) ENCARG(cons_app(false, len)) -> c12(APP(false, len), ENCARG(false)) ENCARG(cons_app(filter, len)) -> c12(APP(filter, len), ENCARG(filter)) ENCARG(cons_app(len, len)) -> c12(APP(len, len), ENCARG(len)) ENCARG(cons_app(cons, len)) -> c12(APP(cons, len), ENCARG(cons)) ENCARG(cons_app(s, len)) -> c12(APP(s, len), ENCARG(s)) ENCARG(cons_app(if, len)) -> c12(APP(if, len), ENCARG(if)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c12(APP(encArg(x0), nil), ENCARG(x0)) by ENCARG(cons_app(if, nil)) -> c12(APP(if, nil), ENCARG(if)) ENCARG(cons_app(true, nil)) -> c12(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c12(APP(false, nil), ENCARG(false)) ENCARG(cons_app(sub, nil)) -> c12(APP(sub, nil), ENCARG(sub)) ENCARG(cons_app(0, nil)) -> c12(APP(0, nil), ENCARG(0)) ENCARG(cons_app(s, nil)) -> c12(APP(s, nil), ENCARG(s)) ENCARG(cons_app(gtr, nil)) -> c12(APP(gtr, nil), ENCARG(gtr)) ENCARG(cons_app(d, nil)) -> c12(APP(d, nil), ENCARG(d)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil), ENCARG(len)) ENCARG(cons_app(nil, nil)) -> c12(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c12(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(filter, nil)) -> c12(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), nil)) -> c12(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(if, nil)) -> c12(APP(if, nil), ENCARG(if)) ENCARG(cons_app(true, nil)) -> c12(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c12(APP(false, nil), ENCARG(false)) ENCARG(cons_app(sub, nil)) -> c12(APP(sub, nil), ENCARG(sub)) ENCARG(cons_app(0, nil)) -> c12(APP(0, nil), ENCARG(0)) ENCARG(cons_app(s, nil)) -> c12(APP(s, nil), ENCARG(s)) ENCARG(cons_app(gtr, nil)) -> c12(APP(gtr, nil), ENCARG(gtr)) ENCARG(cons_app(d, nil)) -> c12(APP(d, nil), ENCARG(d)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil), ENCARG(len)) ENCARG(cons_app(nil, nil)) -> c12(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c12(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(filter, nil)) -> c12(APP(filter, nil), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 11 trailing nodes: ENCARG(cons_app(s, nil)) -> c12(APP(s, nil), ENCARG(s)) ENCARG(cons_app(nil, nil)) -> c12(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(0, nil)) -> c12(APP(0, nil), ENCARG(0)) ENCARG(cons_app(false, nil)) -> c12(APP(false, nil), ENCARG(false)) ENCARG(cons_app(gtr, nil)) -> c12(APP(gtr, nil), ENCARG(gtr)) ENCARG(cons_app(cons, nil)) -> c12(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(true, nil)) -> c12(APP(true, nil), ENCARG(true)) ENCARG(cons_app(filter, nil)) -> c12(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(d, nil)) -> c12(APP(d, nil), ENCARG(d)) ENCARG(cons_app(sub, nil)) -> c12(APP(sub, nil), ENCARG(sub)) ENCARG(cons_app(if, nil)) -> c12(APP(if, nil), ENCARG(if)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil), ENCARG(len)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c12(APP(encArg(x0), cons), ENCARG(x0)) by ENCARG(cons_app(if, cons)) -> c12(APP(if, cons), ENCARG(if)) ENCARG(cons_app(true, cons)) -> c12(APP(true, cons), ENCARG(true)) ENCARG(cons_app(false, cons)) -> c12(APP(false, cons), ENCARG(false)) ENCARG(cons_app(sub, cons)) -> c12(APP(sub, cons), ENCARG(sub)) ENCARG(cons_app(0, cons)) -> c12(APP(0, cons), ENCARG(0)) ENCARG(cons_app(s, cons)) -> c12(APP(s, cons), ENCARG(s)) ENCARG(cons_app(gtr, cons)) -> c12(APP(gtr, cons), ENCARG(gtr)) ENCARG(cons_app(d, cons)) -> c12(APP(d, cons), ENCARG(d)) ENCARG(cons_app(len, cons)) -> c12(APP(len, cons), ENCARG(len)) ENCARG(cons_app(nil, cons)) -> c12(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c12(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(filter, cons)) -> c12(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), cons)) -> c12(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) ENCARG(cons_app(if, cons)) -> c12(APP(if, cons), ENCARG(if)) ENCARG(cons_app(true, cons)) -> c12(APP(true, cons), ENCARG(true)) ENCARG(cons_app(false, cons)) -> c12(APP(false, cons), ENCARG(false)) ENCARG(cons_app(sub, cons)) -> c12(APP(sub, cons), ENCARG(sub)) ENCARG(cons_app(0, cons)) -> c12(APP(0, cons), ENCARG(0)) ENCARG(cons_app(s, cons)) -> c12(APP(s, cons), ENCARG(s)) ENCARG(cons_app(gtr, cons)) -> c12(APP(gtr, cons), ENCARG(gtr)) ENCARG(cons_app(d, cons)) -> c12(APP(d, cons), ENCARG(d)) ENCARG(cons_app(len, cons)) -> c12(APP(len, cons), ENCARG(len)) ENCARG(cons_app(nil, cons)) -> c12(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c12(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(filter, cons)) -> c12(APP(filter, cons), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(s, cons)) -> c12(APP(s, cons), ENCARG(s)) ENCARG(cons_app(true, cons)) -> c12(APP(true, cons), ENCARG(true)) ENCARG(cons_app(filter, cons)) -> c12(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(d, cons)) -> c12(APP(d, cons), ENCARG(d)) ENCARG(cons_app(sub, cons)) -> c12(APP(sub, cons), ENCARG(sub)) ENCARG(cons_app(len, cons)) -> c12(APP(len, cons), ENCARG(len)) ENCARG(cons_app(if, cons)) -> c12(APP(if, cons), ENCARG(if)) ENCARG(cons_app(nil, cons)) -> c12(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(gtr, cons)) -> c12(APP(gtr, cons), ENCARG(gtr)) ENCARG(cons_app(cons, cons)) -> c12(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(0, cons)) -> c12(APP(0, cons), ENCARG(0)) ENCARG(cons_app(false, cons)) -> c12(APP(false, cons), ENCARG(false)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_2, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, filter)) -> c12(APP(encArg(x0), filter), ENCARG(x0)) by ENCARG(cons_app(if, filter)) -> c12(APP(if, filter), ENCARG(if)) ENCARG(cons_app(true, filter)) -> c12(APP(true, filter), ENCARG(true)) ENCARG(cons_app(false, filter)) -> c12(APP(false, filter), ENCARG(false)) ENCARG(cons_app(sub, filter)) -> c12(APP(sub, filter), ENCARG(sub)) ENCARG(cons_app(0, filter)) -> c12(APP(0, filter), ENCARG(0)) ENCARG(cons_app(s, filter)) -> c12(APP(s, filter), ENCARG(s)) ENCARG(cons_app(gtr, filter)) -> c12(APP(gtr, filter), ENCARG(gtr)) ENCARG(cons_app(d, filter)) -> c12(APP(d, filter), ENCARG(d)) ENCARG(cons_app(len, filter)) -> c12(APP(len, filter), ENCARG(len)) ENCARG(cons_app(nil, filter)) -> c12(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(cons, filter)) -> c12(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(filter, filter)) -> c12(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(cons_app(z0, z1), filter)) -> c12(APP(app(encArg(z0), encArg(z1)), filter), ENCARG(cons_app(z0, z1))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) ENCARG(cons_app(if, filter)) -> c12(APP(if, filter), ENCARG(if)) ENCARG(cons_app(true, filter)) -> c12(APP(true, filter), ENCARG(true)) ENCARG(cons_app(false, filter)) -> c12(APP(false, filter), ENCARG(false)) ENCARG(cons_app(sub, filter)) -> c12(APP(sub, filter), ENCARG(sub)) ENCARG(cons_app(0, filter)) -> c12(APP(0, filter), ENCARG(0)) ENCARG(cons_app(s, filter)) -> c12(APP(s, filter), ENCARG(s)) ENCARG(cons_app(gtr, filter)) -> c12(APP(gtr, filter), ENCARG(gtr)) ENCARG(cons_app(d, filter)) -> c12(APP(d, filter), ENCARG(d)) ENCARG(cons_app(len, filter)) -> c12(APP(len, filter), ENCARG(len)) ENCARG(cons_app(nil, filter)) -> c12(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(cons, filter)) -> c12(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(filter, filter)) -> c12(APP(filter, filter), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c12_2, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_app(gtr, filter)) -> c12(APP(gtr, filter), ENCARG(gtr)) ENCARG(cons_app(true, filter)) -> c12(APP(true, filter), ENCARG(true)) ENCARG(cons_app(0, filter)) -> c12(APP(0, filter), ENCARG(0)) ENCARG(cons_app(false, filter)) -> c12(APP(false, filter), ENCARG(false)) ENCARG(cons_app(d, filter)) -> c12(APP(d, filter), ENCARG(d)) ENCARG(cons_app(sub, filter)) -> c12(APP(sub, filter), ENCARG(sub)) ENCARG(cons_app(s, filter)) -> c12(APP(s, filter), ENCARG(s)) ENCARG(cons_app(filter, filter)) -> c12(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(len, filter)) -> c12(APP(len, filter), ENCARG(len)) ENCARG(cons_app(nil, filter)) -> c12(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(if, filter)) -> c12(APP(if, filter), ENCARG(if)) ENCARG(cons_app(cons, filter)) -> c12(APP(cons, filter), ENCARG(cons)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c12_2, c34_4, c1_1, c38_4, c38_3, c_1, c12_3 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(len, x1)) -> c12(APP(len, encArg(x1)), ENCARG(x1)) by ENCARG(cons_app(len, if)) -> c12(APP(len, if), ENCARG(if)) ENCARG(cons_app(len, true)) -> c12(APP(len, true), ENCARG(true)) ENCARG(cons_app(len, false)) -> c12(APP(len, false), ENCARG(false)) ENCARG(cons_app(len, sub)) -> c12(APP(len, sub), ENCARG(sub)) ENCARG(cons_app(len, 0)) -> c12(APP(len, 0), ENCARG(0)) ENCARG(cons_app(len, s)) -> c12(APP(len, s), ENCARG(s)) ENCARG(cons_app(len, gtr)) -> c12(APP(len, gtr), ENCARG(gtr)) ENCARG(cons_app(len, d)) -> c12(APP(len, d), ENCARG(d)) ENCARG(cons_app(len, len)) -> c12(APP(len, len), ENCARG(len)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil), ENCARG(nil)) ENCARG(cons_app(len, cons)) -> c12(APP(len, cons), ENCARG(cons)) ENCARG(cons_app(len, filter)) -> c12(APP(len, filter), ENCARG(filter)) ENCARG(cons_app(len, cons_app(z0, z1))) -> c12(APP(len, app(encArg(z0), encArg(z1))), ENCARG(cons_app(z0, z1))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) ENCARG(cons_app(len, if)) -> c12(APP(len, if), ENCARG(if)) ENCARG(cons_app(len, true)) -> c12(APP(len, true), ENCARG(true)) ENCARG(cons_app(len, false)) -> c12(APP(len, false), ENCARG(false)) ENCARG(cons_app(len, sub)) -> c12(APP(len, sub), ENCARG(sub)) ENCARG(cons_app(len, 0)) -> c12(APP(len, 0), ENCARG(0)) ENCARG(cons_app(len, s)) -> c12(APP(len, s), ENCARG(s)) ENCARG(cons_app(len, gtr)) -> c12(APP(len, gtr), ENCARG(gtr)) ENCARG(cons_app(len, d)) -> c12(APP(len, d), ENCARG(d)) ENCARG(cons_app(len, len)) -> c12(APP(len, len), ENCARG(len)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil), ENCARG(nil)) ENCARG(cons_app(len, cons)) -> c12(APP(len, cons), ENCARG(cons)) ENCARG(cons_app(len, filter)) -> c12(APP(len, filter), ENCARG(filter)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3, c12_2 ---------------------------------------- (123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 11 trailing nodes: ENCARG(cons_app(len, 0)) -> c12(APP(len, 0), ENCARG(0)) ENCARG(cons_app(len, filter)) -> c12(APP(len, filter), ENCARG(filter)) ENCARG(cons_app(len, false)) -> c12(APP(len, false), ENCARG(false)) ENCARG(cons_app(len, gtr)) -> c12(APP(len, gtr), ENCARG(gtr)) ENCARG(cons_app(len, s)) -> c12(APP(len, s), ENCARG(s)) ENCARG(cons_app(len, len)) -> c12(APP(len, len), ENCARG(len)) ENCARG(cons_app(len, true)) -> c12(APP(len, true), ENCARG(true)) ENCARG(cons_app(len, if)) -> c12(APP(len, if), ENCARG(if)) ENCARG(cons_app(len, cons)) -> c12(APP(len, cons), ENCARG(cons)) ENCARG(cons_app(len, d)) -> c12(APP(len, d), ENCARG(d)) ENCARG(cons_app(len, sub)) -> c12(APP(len, sub), ENCARG(sub)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil), ENCARG(nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3, c12_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3, c12_2 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) by APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3, c12_2 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) by APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3, c12_2 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0))), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) by APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c34_4, c1_1, c38_4, c38_3, c_1, c12_3, c12_2 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0)))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) by APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, z1), z0)), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1))), APP(app(gtr, app(s, z1)), app(s, z0)), APP(app(d, app(s, app(s, z1))), app(app(sub, app(s, z0)), app(s, z1))), APP(app(sub, app(s, z0)), app(s, z1))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) by APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(filter, len), nil))), nil), APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), nil))), nil), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(filter, len), nil))), nil), APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), nil))), nil), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(filter, len), nil))), nil), APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), nil))), nil), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4 ---------------------------------------- (139) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) by APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(filter, len), app(app(cons, x2), x3)))), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), app(app(cons, x2), x3)))), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(filter, len), app(app(cons, x2), x3)))), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), app(app(cons, x2), x3)))), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(filter, len), app(app(cons, x2), x3)))), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), app(app(cons, x2), x3)))), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil)), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) by APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(app(app(if, 0), app(app(cons, nil), nil)), app(app(filter, len), nil)), APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), nil)), app(app(filter, len), nil)), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(app(if, nil), app(app(cons, nil), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(app(app(if, 0), app(app(cons, nil), nil)), app(app(filter, len), nil)), APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), nil)), app(app(filter, len), nil)), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(app(if, nil), app(app(cons, nil), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(app(app(if, 0), app(app(cons, nil), nil)), app(app(filter, len), nil)), APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), nil)), app(app(filter, len), nil)), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(app(if, nil), app(app(cons, nil), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), nil), APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c38(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), nil), APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), nil), APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), nil), APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c38(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), nil), APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), nil), APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c38(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), nil), APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), nil), APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c38(APP(len, nil), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), nil), APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1 ---------------------------------------- (149) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) by APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, x2), x3))), APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, x2), x3))), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, x2), x3))), APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, x2), x3))), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, 0), app(app(cons, nil), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, x2), x3))), APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(app(if, app(len, x2)), app(app(cons, x2), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, x2), x3))), APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(app(if, nil), app(app(cons, nil), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) by APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil), APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), nil), APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), app(app(cons, z1), z2)))), app(app(app(if, app(app(sub, app(s, x0)), z1)), app(app(cons, z1), app(app(filter, app(sub, app(s, x0))), z2))), app(app(filter, app(sub, app(s, x0))), z2))), APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), app(app(cons, z1), z2)), APP(app(filter, app(sub, app(s, x0))), app(app(cons, z1), z2))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil)), APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), nil), APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(app(if, app(app(sub, app(s, x0)), z1)), app(app(cons, z1), app(app(filter, app(sub, app(s, x0))), z2))), app(app(filter, app(sub, app(s, x0))), z2)))), app(app(filter, app(sub, app(s, x0))), app(app(cons, z1), z2))), APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), app(app(cons, z1), z2)), APP(app(filter, app(sub, app(s, x0))), app(app(cons, z1), z2))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil), APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), nil), APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil)), APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), nil), APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil), APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), nil), APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil)), APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), nil), APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1 ---------------------------------------- (157) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1, c4_1 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) by APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil), APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), nil), APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), app(app(cons, z1), z2)))), app(app(app(if, app(app(gtr, app(s, x0)), z1)), app(app(cons, z1), app(app(filter, app(gtr, app(s, x0))), z2))), app(app(filter, app(gtr, app(s, x0))), z2))), APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), app(app(cons, z1), z2)), APP(app(filter, app(gtr, app(s, x0))), app(app(cons, z1), z2))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil)), APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), nil), APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(app(if, app(app(gtr, app(s, x0)), z1)), app(app(cons, z1), app(app(filter, app(gtr, app(s, x0))), z2))), app(app(filter, app(gtr, app(s, x0))), z2)))), app(app(filter, app(gtr, app(s, x0))), app(app(cons, z1), z2))), APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), app(app(cons, z1), z2)), APP(app(filter, app(gtr, app(s, x0))), app(app(cons, z1), z2))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil), APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), nil), APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil)), APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), nil), APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil), APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), nil), APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil)), APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), nil), APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1, c4_1 ---------------------------------------- (161) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1, c4_1, c5_1 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2)), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), x2), APP(app(filter, app(d, app(s, z0))), x2)) by APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), nil))), nil), APP(app(d, app(s, x0)), app(s, x1)), APP(app(filter, app(d, app(s, x0))), nil), APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), app(app(cons, z1), z2)))), app(app(app(if, app(app(d, app(s, x0)), z1)), app(app(cons, z1), app(app(filter, app(d, app(s, x0))), z2))), app(app(filter, app(d, app(s, x0))), z2))), APP(app(d, app(s, x0)), app(s, x1)), APP(app(filter, app(d, app(s, x0))), app(app(cons, z1), z2)), APP(app(filter, app(d, app(s, x0))), app(app(cons, z1), z2))) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), nil)), app(app(filter, app(d, app(s, x0))), nil)), APP(app(d, app(s, x0)), app(s, x1)), APP(app(filter, app(d, app(s, x0))), nil), APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(app(if, app(app(d, app(s, x0)), z1)), app(app(cons, z1), app(app(filter, app(d, app(s, x0))), z2))), app(app(filter, app(d, app(s, x0))), z2)))), app(app(filter, app(d, app(s, x0))), app(app(cons, z1), z2))), APP(app(d, app(s, x0)), app(s, x1)), APP(app(filter, app(d, app(s, x0))), app(app(cons, z1), z2)), APP(app(filter, app(d, app(s, x0))), app(app(cons, z1), z2))) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z1)))), app(app(cons, app(s, app(s, z0))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1)))), app(app(cons, app(s, app(s, z0))), app(app(filter, app(d, app(s, app(s, z1)))), x2))), app(app(filter, app(d, app(s, app(s, z1)))), x2)), APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(filter, app(d, app(s, app(s, z1)))), x2), APP(app(filter, app(d, app(s, app(s, z1)))), x2)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0)))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, app(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))), app(app(cons, app(s, 0)), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))))), app(app(cons, app(s, app(s, z1))), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(filter, app(d, app(s, x0))), x2), APP(app(filter, app(d, app(s, x0))), x2)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), nil))), nil), APP(app(d, app(s, x0)), app(s, x1)), APP(app(filter, app(d, app(s, x0))), nil), APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), nil)), app(app(filter, app(d, app(s, x0))), nil)), APP(app(d, app(s, x0)), app(s, x1)), APP(app(filter, app(d, app(s, x0))), nil), APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z1)))), app(app(cons, app(s, app(s, z0))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1)))), app(app(cons, app(s, app(s, z0))), app(app(filter, app(d, app(s, app(s, z1)))), x2))), app(app(filter, app(d, app(s, app(s, z1)))), x2)), APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(filter, app(d, app(s, app(s, z1)))), x2), APP(app(filter, app(d, app(s, app(s, z1)))), x2)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0)))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, app(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))), app(app(cons, app(s, 0)), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))))), app(app(cons, app(s, app(s, z1))), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(filter, app(d, app(s, x0))), x2), APP(app(filter, app(d, app(s, x0))), x2)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), nil))), nil), APP(app(d, app(s, x0)), app(s, x1)), APP(app(filter, app(d, app(s, x0))), nil), APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), nil)), app(app(filter, app(d, app(s, x0))), nil)), APP(app(d, app(s, x0)), app(s, x1)), APP(app(filter, app(d, app(s, x0))), nil), APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z1)))), app(app(cons, app(s, app(s, z0))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1)))), app(app(cons, app(s, app(s, z0))), app(app(filter, app(d, app(s, app(s, z1)))), x2))), app(app(filter, app(d, app(s, app(s, z1)))), x2)), APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(filter, app(d, app(s, app(s, z1)))), x2), APP(app(filter, app(d, app(s, app(s, z1)))), x2)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0)))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, app(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))), app(app(cons, app(s, 0)), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))))), app(app(cons, app(s, app(s, z1))), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(filter, app(d, app(s, x0))), x2), APP(app(filter, app(d, app(s, x0))), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1, c4_1, c5_1, c38_2 ---------------------------------------- (165) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z1)))), app(app(cons, app(s, app(s, z0))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1)))), app(app(cons, app(s, app(s, z0))), app(app(filter, app(d, app(s, app(s, z1)))), x2))), app(app(filter, app(d, app(s, app(s, z1)))), x2)), APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(filter, app(d, app(s, app(s, z1)))), x2), APP(app(filter, app(d, app(s, app(s, z1)))), x2)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0)))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, app(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))), app(app(cons, app(s, 0)), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))))), app(app(cons, app(s, app(s, z1))), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(filter, app(d, app(s, x0))), x2), APP(app(filter, app(d, app(s, x0))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), nil))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(d, app(s, x0)), app(s, x1))) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), nil)), app(app(filter, app(d, app(s, x0))), nil))) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z1)))), app(app(cons, app(s, app(s, z0))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1)))), app(app(cons, app(s, app(s, z0))), app(app(filter, app(d, app(s, app(s, z1)))), x2))), app(app(filter, app(d, app(s, app(s, z1)))), x2)), APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(filter, app(d, app(s, app(s, z1)))), x2), APP(app(filter, app(d, app(s, app(s, z1)))), x2)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0)))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, app(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))), app(app(cons, app(s, 0)), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))))), app(app(cons, app(s, app(s, z1))), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(filter, app(d, app(s, x0))), x2), APP(app(filter, app(d, app(s, x0))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), nil))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(d, app(s, x0)), app(s, x1))) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), nil)), app(app(filter, app(d, app(s, x0))), nil))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1, c4_1, c5_1, c38_2, c6_1 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) by APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(x0, x1)), app(app(cons, x1), app(app(filter, x0), x2))), app(app(filter, x0), x2))), app(app(cons, app(app(cons, x1), x2)), app(app(filter, app(filter, x0)), nil))), nil), APP(app(filter, x0), app(app(cons, x1), x2)), APP(app(filter, app(filter, x0)), nil), APP(app(filter, app(filter, x0)), nil)) APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(app(app(if, app(x0, x1)), app(app(cons, x1), app(app(filter, x0), x2))), app(app(filter, x0), x2))), app(app(cons, app(app(cons, x1), x2)), app(app(filter, app(filter, x0)), app(app(cons, z1), z2)))), app(app(app(if, app(app(filter, x0), z1)), app(app(cons, z1), app(app(filter, app(filter, x0)), z2))), app(app(filter, app(filter, x0)), z2))), APP(app(filter, x0), app(app(cons, x1), x2)), APP(app(filter, app(filter, x0)), app(app(cons, z1), z2)), APP(app(filter, app(filter, x0)), app(app(cons, z1), z2))) APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(x0, x1)), app(app(cons, x1), app(app(filter, x0), x2))), app(app(filter, x0), x2))), app(app(cons, app(app(cons, x1), x2)), nil)), app(app(filter, app(filter, x0)), nil)), APP(app(filter, x0), app(app(cons, x1), x2)), APP(app(filter, app(filter, x0)), nil), APP(app(filter, app(filter, x0)), nil)) APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(app(app(if, app(x0, x1)), app(app(cons, x1), app(app(filter, x0), x2))), app(app(filter, x0), x2))), app(app(cons, app(app(cons, x1), x2)), app(app(app(if, app(app(filter, x0), z1)), app(app(cons, z1), app(app(filter, app(filter, x0)), z2))), app(app(filter, app(filter, x0)), z2)))), app(app(filter, app(filter, x0)), app(app(cons, z1), z2))), APP(app(filter, x0), app(app(cons, x1), x2)), APP(app(filter, app(filter, x0)), app(app(cons, z1), z2)), APP(app(filter, app(filter, x0)), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil)), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil))), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, app(app(if, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, true), z0))), x3))), app(app(filter, app(filter, app(app(if, true), z0))), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, true), z0))), x3), APP(app(filter, app(filter, app(app(if, true), z0))), x3)) APP(app(filter, app(filter, app(app(if, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, false), z0))), x3))), app(app(filter, app(filter, app(app(if, false), z0))), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, false), z0))), x3), APP(app(filter, app(filter, app(app(if, false), z0))), x3)) APP(app(filter, app(filter, app(sub, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(sub, z0))), x3))), app(app(filter, app(filter, app(sub, z0))), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(sub, z0))), x3), APP(app(filter, app(filter, app(sub, z0))), x3)) APP(app(filter, app(filter, app(sub, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(sub, app(s, z0)))), x3))), app(app(filter, app(filter, app(sub, app(s, z0)))), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2))), app(app(cons, app(app(cons, z0), x2)), app(app(filter, app(filter, app(gtr, 0))), x3))), app(app(filter, app(filter, app(gtr, 0))), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)), APP(app(filter, app(filter, app(gtr, 0))), x3), APP(app(filter, app(filter, app(gtr, 0))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(d, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(d, z0))), x3))), app(app(filter, app(filter, app(d, z0))), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(d, z0))), x3), APP(app(filter, app(filter, app(d, z0))), x3)) APP(app(filter, app(filter, app(d, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(d, app(s, z0)))), x3))), app(app(filter, app(filter, app(d, app(s, z0)))), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(d, app(s, z0)))), x3), APP(app(filter, app(filter, app(d, app(s, z0)))), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x2))), app(app(filter, len), x2))), app(app(cons, app(app(cons, nil), x2)), app(app(filter, app(filter, len)), x3))), app(app(filter, app(filter, len)), x3)), APP(app(filter, len), app(app(cons, nil), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, app(app(cons, z0), z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x2))), app(app(filter, len), x2))), app(app(cons, app(app(cons, app(app(cons, z0), z1)), x2)), app(app(filter, app(filter, len)), x3))), app(app(filter, app(filter, len)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, nil), x2)), app(app(filter, app(filter, app(filter, z0))), x3))), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3))), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c38(APP(app(filter, app(filter, x0)), x3), APP(app(filter, app(filter, x0)), x3)) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z1)))), app(app(cons, app(s, app(s, z0))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1)))), app(app(cons, app(s, app(s, z0))), app(app(filter, app(d, app(s, app(s, z1)))), x2))), app(app(filter, app(d, app(s, app(s, z1)))), x2)), APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(filter, app(d, app(s, app(s, z1)))), x2), APP(app(filter, app(d, app(s, app(s, z1)))), x2)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0)))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, app(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))), app(app(cons, app(s, 0)), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))))), app(app(cons, app(s, app(s, z1))), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(filter, app(d, app(s, x0))), x2), APP(app(filter, app(d, app(s, x0))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), nil))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(d, app(s, x0)), app(s, x1))) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), nil)), app(app(filter, app(d, app(s, x0))), nil))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil)), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil))), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, app(app(if, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, true), z0))), x3))), app(app(filter, app(filter, app(app(if, true), z0))), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, true), z0))), x3), APP(app(filter, app(filter, app(app(if, true), z0))), x3)) APP(app(filter, app(filter, app(app(if, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, false), z0))), x3))), app(app(filter, app(filter, app(app(if, false), z0))), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, false), z0))), x3), APP(app(filter, app(filter, app(app(if, false), z0))), x3)) APP(app(filter, app(filter, app(sub, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(sub, z0))), x3))), app(app(filter, app(filter, app(sub, z0))), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(sub, z0))), x3), APP(app(filter, app(filter, app(sub, z0))), x3)) APP(app(filter, app(filter, app(sub, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(sub, app(s, z0)))), x3))), app(app(filter, app(filter, app(sub, app(s, z0)))), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2))), app(app(cons, app(app(cons, z0), x2)), app(app(filter, app(filter, app(gtr, 0))), x3))), app(app(filter, app(filter, app(gtr, 0))), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)), APP(app(filter, app(filter, app(gtr, 0))), x3), APP(app(filter, app(filter, app(gtr, 0))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(d, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(d, z0))), x3))), app(app(filter, app(filter, app(d, z0))), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(d, z0))), x3), APP(app(filter, app(filter, app(d, z0))), x3)) APP(app(filter, app(filter, app(d, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(d, app(s, z0)))), x3))), app(app(filter, app(filter, app(d, app(s, z0)))), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(d, app(s, z0)))), x3), APP(app(filter, app(filter, app(d, app(s, z0)))), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x2))), app(app(filter, len), x2))), app(app(cons, app(app(cons, nil), x2)), app(app(filter, app(filter, len)), x3))), app(app(filter, app(filter, len)), x3)), APP(app(filter, len), app(app(cons, nil), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, app(app(cons, z0), z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x2))), app(app(filter, len), x2))), app(app(cons, app(app(cons, app(app(cons, z0), z1)), x2)), app(app(filter, app(filter, len)), x3))), app(app(filter, app(filter, len)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, nil), x2)), app(app(filter, app(filter, app(filter, z0))), x3))), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3))), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c38(APP(app(filter, app(filter, x0)), x3), APP(app(filter, app(filter, x0)), x3)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z1)))), app(app(cons, app(s, app(s, z0))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1)))), app(app(cons, app(s, app(s, z0))), app(app(filter, app(d, app(s, app(s, z1)))), x2))), app(app(filter, app(d, app(s, app(s, z1)))), x2)), APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(filter, app(d, app(s, app(s, z1)))), x2), APP(app(filter, app(d, app(s, app(s, z1)))), x2)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0)))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, app(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))), app(app(cons, app(s, 0)), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))))), app(app(cons, app(s, app(s, z1))), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(filter, app(d, app(s, x0))), x2), APP(app(filter, app(d, app(s, x0))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), nil))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(d, app(s, x0)), app(s, x1))) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), nil)), app(app(filter, app(d, app(s, x0))), nil))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil)), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil))), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, app(app(if, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, true), z0))), x3))), app(app(filter, app(filter, app(app(if, true), z0))), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, true), z0))), x3), APP(app(filter, app(filter, app(app(if, true), z0))), x3)) APP(app(filter, app(filter, app(app(if, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, false), z0))), x3))), app(app(filter, app(filter, app(app(if, false), z0))), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, false), z0))), x3), APP(app(filter, app(filter, app(app(if, false), z0))), x3)) APP(app(filter, app(filter, app(sub, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(sub, z0))), x3))), app(app(filter, app(filter, app(sub, z0))), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(sub, z0))), x3), APP(app(filter, app(filter, app(sub, z0))), x3)) APP(app(filter, app(filter, app(sub, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(sub, app(s, z0)))), x3))), app(app(filter, app(filter, app(sub, app(s, z0)))), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2))), app(app(cons, app(app(cons, z0), x2)), app(app(filter, app(filter, app(gtr, 0))), x3))), app(app(filter, app(filter, app(gtr, 0))), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)), APP(app(filter, app(filter, app(gtr, 0))), x3), APP(app(filter, app(filter, app(gtr, 0))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(d, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(d, z0))), x3))), app(app(filter, app(filter, app(d, z0))), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(d, z0))), x3), APP(app(filter, app(filter, app(d, z0))), x3)) APP(app(filter, app(filter, app(d, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(d, app(s, z0)))), x3))), app(app(filter, app(filter, app(d, app(s, z0)))), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(d, app(s, z0)))), x3), APP(app(filter, app(filter, app(d, app(s, z0)))), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x2))), app(app(filter, len), x2))), app(app(cons, app(app(cons, nil), x2)), app(app(filter, app(filter, len)), x3))), app(app(filter, app(filter, len)), x3)), APP(app(filter, len), app(app(cons, nil), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, app(app(cons, z0), z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x2))), app(app(filter, len), x2))), app(app(cons, app(app(cons, app(app(cons, z0), z1)), x2)), app(app(filter, app(filter, len)), x3))), app(app(filter, app(filter, len)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, nil), x2)), app(app(filter, app(filter, app(filter, z0))), x3))), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3))), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c38(APP(app(filter, app(filter, x0)), x3), APP(app(filter, app(filter, x0)), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1, c4_1, c5_1, c38_2, c6_1 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: encArg(if) -> if encArg(true) -> true encArg(false) -> false encArg(sub) -> sub encArg(0) -> 0 encArg(s) -> s encArg(gtr) -> gtr encArg(d) -> d encArg(len) -> len encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(app(sub, z0), 0) -> z0 app(app(sub, app(s, z0)), app(s, z1)) -> app(app(sub, z0), z1) app(app(gtr, 0), z0) -> false app(app(gtr, app(s, z0)), 0) -> true app(app(gtr, app(s, z0)), app(s, z1)) -> app(app(gtr, z0), z1) app(app(d, z0), 0) -> true app(app(d, app(s, z0)), app(s, z1)) -> app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0))) app(len, nil) -> 0 app(len, app(app(cons, z0), z1)) -> app(s, app(len, z1)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)) Tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) ENCARG(cons_app(if, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(sub, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(gtr, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(d, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c12(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c12(ENCARG(x1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, sub) -> c(APP(encArg(x0), sub)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, gtr) -> c(APP(encArg(x0), gtr)) ENCODE_APP(x0, d) -> c(APP(encArg(x0), d)) ENCODE_APP(x0, len) -> c(APP(encArg(x0), len)) 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, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(len, x1) -> c(APP(len, 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, if))) -> c12(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c12(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c12(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, sub))) -> c12(APP(encArg(x0), app(encArg(x1), sub)), ENCARG(x0), ENCARG(cons_app(x1, sub))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c12(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c12(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, gtr))) -> c12(APP(encArg(x0), app(encArg(x1), gtr)), ENCARG(x0), ENCARG(cons_app(x1, gtr))) ENCARG(cons_app(x0, cons_app(x1, d))) -> c12(APP(encArg(x0), app(encArg(x1), d)), ENCARG(x0), ENCARG(cons_app(x1, d))) ENCARG(cons_app(x0, cons_app(x1, len))) -> c12(APP(encArg(x0), app(encArg(x1), len)), ENCARG(x0), ENCARG(cons_app(x1, len))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c12(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c12(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c12(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c12(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(if, x2))) -> c12(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c12(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c12(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(sub, x2))) -> c12(APP(encArg(x0), app(sub, encArg(x2))), ENCARG(x0), ENCARG(cons_app(sub, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c12(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c12(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(gtr, x2))) -> c12(APP(encArg(x0), app(gtr, encArg(x2))), ENCARG(x0), ENCARG(cons_app(gtr, x2))) ENCARG(cons_app(x0, cons_app(d, x2))) -> c12(APP(encArg(x0), app(d, encArg(x2))), ENCARG(x0), ENCARG(cons_app(d, x2))) ENCARG(cons_app(x0, cons_app(len, x2))) -> c12(APP(encArg(x0), app(len, encArg(x2))), ENCARG(x0), ENCARG(cons_app(len, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c12(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c12(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c12(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c12(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))) -> c12(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(sub, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(gtr, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(d, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(len, cons_app(x1, x2))) -> c12(APP(len, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c12(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, if), x2)) -> c12(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c12(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c12(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, sub), x2)) -> c12(APP(app(encArg(x0), sub), encArg(x2)), ENCARG(cons_app(x0, sub)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c12(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c12(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, gtr), x2)) -> c12(APP(app(encArg(x0), gtr), encArg(x2)), ENCARG(cons_app(x0, gtr)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, d), x2)) -> c12(APP(app(encArg(x0), d), encArg(x2)), ENCARG(cons_app(x0, d)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, len), x2)) -> c12(APP(app(encArg(x0), len), encArg(x2)), ENCARG(cons_app(x0, len)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c12(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c12(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c12(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c12(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(sub, x1), x2)) -> c12(APP(app(sub, encArg(x1)), encArg(x2)), ENCARG(cons_app(sub, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(gtr, x1), x2)) -> c12(APP(app(gtr, encArg(x1)), encArg(x2)), ENCARG(cons_app(gtr, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(d, x1), x2)) -> c12(APP(app(d, encArg(x1)), encArg(x2)), ENCARG(cons_app(d, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(len, x1), x2)) -> c12(APP(app(len, encArg(x1)), encArg(x2)), ENCARG(cons_app(len, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c12(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)) -> c12(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), if)) -> c12(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c12(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c12(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), sub)) -> c12(APP(app(encArg(x0), encArg(x1)), sub), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c12(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c12(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), gtr)) -> c12(APP(app(encArg(x0), encArg(x1)), gtr), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), d)) -> c12(APP(app(encArg(x0), encArg(x1)), d), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), len)) -> c12(APP(app(encArg(x0), encArg(x1)), len), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c12(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c12(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c12(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(if, x1), x2)) -> c12(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c12(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c12(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c12(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c12(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c12(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c12(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(len, nil)) -> c12(APP(len, nil)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z1)))), app(app(cons, app(s, app(s, z0))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1)))), app(app(cons, app(s, app(s, z0))), app(app(filter, app(d, app(s, app(s, z1)))), x2))), app(app(filter, app(d, app(s, app(s, z1)))), x2)), APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(filter, app(d, app(s, app(s, z1)))), x2), APP(app(filter, app(d, app(s, app(s, z1)))), x2)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0)))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, app(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))), app(app(cons, app(s, 0)), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))))), app(app(cons, app(s, app(s, z1))), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(filter, app(d, app(s, x0))), x2), APP(app(filter, app(d, app(s, x0))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), nil))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(d, app(s, x0)), app(s, x1))) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), nil)), app(app(filter, app(d, app(s, x0))), nil))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil)), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil))), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, app(app(if, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, true), z0))), x3))), app(app(filter, app(filter, app(app(if, true), z0))), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, true), z0))), x3), APP(app(filter, app(filter, app(app(if, true), z0))), x3)) APP(app(filter, app(filter, app(app(if, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, false), z0))), x3))), app(app(filter, app(filter, app(app(if, false), z0))), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, false), z0))), x3), APP(app(filter, app(filter, app(app(if, false), z0))), x3)) APP(app(filter, app(filter, app(sub, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(sub, z0))), x3))), app(app(filter, app(filter, app(sub, z0))), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(sub, z0))), x3), APP(app(filter, app(filter, app(sub, z0))), x3)) APP(app(filter, app(filter, app(sub, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(sub, app(s, z0)))), x3))), app(app(filter, app(filter, app(sub, app(s, z0)))), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2))), app(app(cons, app(app(cons, z0), x2)), app(app(filter, app(filter, app(gtr, 0))), x3))), app(app(filter, app(filter, app(gtr, 0))), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)), APP(app(filter, app(filter, app(gtr, 0))), x3), APP(app(filter, app(filter, app(gtr, 0))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(d, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(d, z0))), x3))), app(app(filter, app(filter, app(d, z0))), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(d, z0))), x3), APP(app(filter, app(filter, app(d, z0))), x3)) APP(app(filter, app(filter, app(d, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(d, app(s, z0)))), x3))), app(app(filter, app(filter, app(d, app(s, z0)))), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(d, app(s, z0)))), x3), APP(app(filter, app(filter, app(d, app(s, z0)))), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3))), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c38(APP(app(filter, app(filter, x0)), x3), APP(app(filter, app(filter, x0)), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(filter, len), app(app(cons, nil), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, app(app(cons, z0), z1)), x2)), x3)) -> c38(APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) S tuples: APP(app(app(if, true), z0), z1) -> c26 APP(app(app(if, false), z0), z1) -> c27 APP(app(sub, z0), 0) -> c28 APP(app(gtr, 0), z0) -> c30 APP(app(gtr, app(s, z0)), 0) -> c31 APP(app(d, z0), 0) -> c33 APP(len, nil) -> c35 APP(app(filter, z0), nil) -> c37 APP(app(sub, app(s, z0)), app(s, z1)) -> c29(APP(app(sub, z0), z1)) APP(app(gtr, app(s, z0)), app(s, z1)) -> c32(APP(app(gtr, z0), z1)) APP(len, app(app(cons, z0), z1)) -> c36(APP(len, z1)) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))) APP(app(d, app(s, app(s, z0))), app(s, 0)) -> c1(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2)), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), x2), APP(app(filter, app(app(if, true), z0)), x2)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2)), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), x2), APP(app(filter, app(app(if, false), z0)), x2)) APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2)), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), x2), APP(app(filter, app(sub, z0)), x2)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2)), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), x2), APP(app(filter, app(gtr, 0)), x2)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2)), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), x2), APP(app(filter, app(gtr, app(s, z0))), x2)) APP(app(filter, app(d, z0)), app(app(cons, 0), x2)) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2)), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), x2), APP(app(filter, app(d, z0)), x2)) APP(app(filter, len), app(app(cons, nil), x2)) -> c38(APP(len, nil), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), x2), APP(app(filter, len), x2)) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), x2), APP(app(filter, app(filter, z0)), x2)) APP(app(d, app(s, 0)), app(s, 0)) -> c34(APP(app(app(if, app(app(gtr, 0), 0)), false), true), APP(app(gtr, 0), 0), APP(app(d, app(s, 0)), app(app(sub, 0), 0)), APP(app(sub, 0), 0)) APP(app(d, app(s, 0)), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, 0), app(s, z1))), false), app(app(app(if, app(app(gtr, 0), z1)), false), app(app(d, app(s, 0)), app(app(sub, z1), 0)))), APP(app(gtr, 0), app(s, z1)), APP(app(d, app(s, 0)), app(app(sub, app(s, z1)), 0)), APP(app(sub, app(s, z1)), 0)) APP(app(d, app(s, 0)), app(s, z0)) -> c34(APP(app(app(if, false), false), app(app(d, app(s, 0)), z0)), APP(app(gtr, 0), z0), APP(app(d, app(s, 0)), app(app(sub, z0), 0)), APP(app(sub, z0), 0)) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, app(app(gtr, app(s, 0)), app(s, z0))), false), app(app(d, app(s, app(s, 0))), z0)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z1)))), app(s, app(s, app(s, z0)))) -> c34(APP(app(app(if, app(app(gtr, app(s, app(s, z1))), app(s, app(s, z0)))), false), app(app(d, app(s, app(s, app(s, z1)))), app(app(sub, z0), z1))), APP(app(gtr, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(d, app(s, app(s, app(s, z1)))), app(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1)))) APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, z1), z0))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))), APP(app(sub, app(s, z1)), app(s, z0))) APP(app(d, app(s, app(s, 0))), app(s, app(s, z0))) -> c34(APP(app(app(if, false), false), app(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0)))), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(d, app(s, app(s, 0))), app(app(sub, app(s, z0)), app(s, 0))), APP(app(sub, app(s, z0)), app(s, 0))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, 0))) -> c34(APP(app(app(if, true), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, 0)), app(s, app(s, z0)))), APP(app(sub, app(s, 0)), app(s, app(s, z0)))) APP(app(d, app(s, app(s, app(s, z0)))), app(s, app(s, app(s, z1)))) -> c34(APP(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0))))), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(d, app(s, app(s, app(s, z0)))), app(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))), APP(app(sub, app(s, app(s, z1))), app(s, app(s, z0)))) APP(app(filter, z0), app(app(cons, x1), nil)) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), nil), APP(z0, x1), APP(app(filter, z0), nil), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), nil))), nil), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), nil))), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), nil))), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c2(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), nil))), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), nil))), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), nil))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c2(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), nil))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), nil))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c2(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), nil))), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c2(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c2(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c2(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil)), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), nil)))), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))))), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)))), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)))), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(filter, app(sub, z0)), app(app(cons, 0), x3)))), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3)))), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(filter, app(d, z0)), app(app(cons, 0), x3)))), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)))), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, nil), x3)))), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)))), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, nil), x3)))), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)))), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), APP(z0, x1), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)))), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), app(app(cons, x2), x3)))), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(len, nil), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), app(app(cons, x2), x3))) -> c38(APP(len, app(app(cons, z0), z1)), APP(app(filter, len), app(app(cons, x2), x3)), APP(app(filter, len), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c38(APP(app(filter, z0), nil), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), nil)), app(app(filter, app(filter, z0)), nil)), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), nil), APP(app(filter, app(filter, z0)), nil)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z0), app(app(cons, z1), nil)), app(app(filter, app(app(if, true), z0)), nil))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, true), z0)), nil)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, z1), app(app(cons, z1), nil)), app(app(filter, app(app(if, false), z0)), nil))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(app(if, false), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), nil)) -> c3(APP(app(filter, app(app(if, false), z0)), nil)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, z0), app(app(cons, 0), nil)), app(app(filter, app(sub, z0)), nil))) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(sub, z0), 0)) APP(app(filter, app(sub, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(sub, z0)), nil)) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(sub, app(s, z0))), nil))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(sub, app(s, z0)), app(s, z1))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(sub, app(s, z0))), nil)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(app(if, false), app(app(cons, z0), nil)), app(app(filter, app(gtr, 0)), nil))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(gtr, 0), z0)) APP(app(filter, app(gtr, 0)), app(app(cons, z0), nil)) -> c3(APP(app(filter, app(gtr, 0)), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(gtr, app(s, z0)), 0)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), nil)), app(app(filter, app(gtr, app(s, z0))), nil))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(gtr, app(s, z0)), app(s, z1))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(gtr, app(s, z0))), nil)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(app(if, true), app(app(cons, 0), nil)), app(app(filter, app(d, z0)), nil))) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(d, z0), 0)) APP(app(filter, app(d, z0)), app(app(cons, 0), nil)) -> c3(APP(app(filter, app(d, z0)), nil)) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), nil)), app(app(filter, app(d, app(s, z0))), nil))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(d, app(s, z0)), app(s, z1))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), nil)) -> c3(APP(app(filter, app(d, app(s, z0))), nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(len, nil)) APP(app(filter, len), app(app(cons, nil), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(len, app(app(cons, z0), z1))) APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), nil)) -> c3(APP(app(filter, len), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, nil), nil)) -> c3(APP(app(filter, app(filter, z0)), nil)) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), nil))), nil))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), nil)), app(app(filter, z0), nil)))), app(app(filter, z0), app(app(cons, x2), nil))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), nil)), APP(app(filter, z0), app(app(cons, x2), nil))) APP(app(filter, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c38(APP(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, x2)), app(app(cons, x2), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2))))), app(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))), APP(z0, x1), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2))), APP(app(filter, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(filter, app(app(if, true), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, true), z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))), APP(app(app(if, true), z0), x1), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, x1), app(app(cons, z1), x3))) -> c38(APP(app(app(if, app(app(app(if, false), z0), x1)), app(app(cons, x1), app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))), APP(app(app(if, false), z0), x1), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x3))) APP(app(filter, app(sub, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(sub, z0), x1)), app(app(cons, x1), app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, 0), x3))), APP(app(sub, z0), x1), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(sub, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(sub, app(s, z0)), x1), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, x1), app(app(cons, z0), x3))) -> c38(APP(app(app(if, app(app(gtr, 0), x1)), app(app(cons, x1), app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, z0), x3))), APP(app(gtr, 0), x1), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(gtr, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(gtr, app(s, z0)), x1), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, app(d, z0)), app(app(cons, x1), app(app(cons, 0), x3))) -> c38(APP(app(app(if, app(app(d, z0), x1)), app(app(cons, x1), app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, 0), x3))), APP(app(d, z0), x1), APP(app(filter, app(d, z0)), app(app(cons, 0), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, x1), app(app(cons, app(s, z1)), x3))) -> c38(APP(app(app(if, app(app(d, app(s, z0)), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))), APP(app(d, app(s, z0)), x1), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, 0), app(app(cons, nil), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, nil), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, nil), x3)), APP(app(filter, len), app(app(cons, nil), x3))) APP(app(filter, len), app(app(cons, x1), app(app(cons, app(app(cons, z0), z1)), x3))) -> c38(APP(app(app(if, app(len, x1)), app(app(cons, x1), app(app(app(if, app(s, app(len, z1))), app(app(cons, app(app(cons, z0), z1)), app(app(filter, len), x3))), app(app(filter, len), x3)))), app(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))), APP(len, x1), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3)), APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, nil), app(app(cons, nil), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, nil), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3)), APP(app(filter, app(filter, z0)), app(app(cons, nil), x3))) APP(app(filter, app(filter, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c38(APP(app(app(if, app(app(filter, z0), x1)), app(app(cons, x1), app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))), APP(app(filter, z0), x1), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, z1), app(app(app(if, app(app(app(if, true), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, true), z0)), x3))), app(app(filter, app(app(if, true), z0)), x3)))), app(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))), APP(app(app(if, true), z0), z1), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, x2), x3))) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z1), app(app(cons, z1), app(app(app(if, app(app(app(if, false), z0), x2)), app(app(cons, x2), app(app(filter, app(app(if, false), z0)), x3))), app(app(filter, app(app(if, false), z0)), x3)))), app(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))), APP(app(app(if, false), z0), z1), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, z0), app(app(cons, 0), app(app(app(if, app(app(sub, z0), x2)), app(app(cons, x2), app(app(filter, app(sub, z0)), x3))), app(app(filter, app(sub, z0)), x3)))), app(app(filter, app(sub, z0)), app(app(cons, x2), x3))), APP(app(sub, z0), 0), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3)), APP(app(filter, app(sub, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(sub, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(sub, app(s, z0))), x3))), app(app(filter, app(sub, app(s, z0))), x3)))), app(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))), APP(app(sub, app(s, z0)), app(s, z1)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, 0)), app(app(cons, z0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, false), app(app(cons, z0), app(app(app(if, app(app(gtr, 0), x2)), app(app(cons, x2), app(app(filter, app(gtr, 0)), x3))), app(app(filter, app(gtr, 0)), x3)))), app(app(filter, app(gtr, 0)), app(app(cons, x2), x3))), APP(app(gtr, 0), z0), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), 0), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(app(if, app(app(gtr, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(gtr, app(s, z0))), x3))), app(app(filter, app(gtr, app(s, z0))), x3)))), app(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))), APP(app(gtr, app(s, z0)), app(s, z1)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(d, z0)), app(app(cons, 0), app(app(cons, x2), x3))) -> c38(APP(app(app(if, true), app(app(cons, 0), app(app(app(if, app(app(d, z0), x2)), app(app(cons, x2), app(app(filter, app(d, z0)), x3))), app(app(filter, app(d, z0)), x3)))), app(app(filter, app(d, z0)), app(app(cons, x2), x3))), APP(app(d, z0), 0), APP(app(filter, app(d, z0)), app(app(cons, x2), x3)), APP(app(filter, app(d, z0)), app(app(cons, x2), x3))) APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(app(if, app(app(d, app(s, z0)), x2)), app(app(cons, x2), app(app(filter, app(d, app(s, z0))), x3))), app(app(filter, app(d, app(s, z0))), x3)))), app(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))), APP(app(d, app(s, z0)), app(s, z1)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, x2), x3))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c38(APP(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(app(if, app(app(filter, z0), x2)), app(app(cons, x2), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)))), app(app(filter, app(filter, z0)), app(app(cons, x2), x3))), APP(app(filter, z0), app(app(cons, z1), z2)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3)), APP(app(filter, app(filter, z0)), app(app(cons, x2), x3))) APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, z0), app(app(cons, app(s, 0)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2)), APP(app(sub, app(s, z0)), app(s, 0)), APP(app(filter, app(sub, app(s, z0))), x2), APP(app(filter, app(sub, app(s, z0))), x2)) APP(app(filter, app(sub, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(sub, app(s, app(s, z0)))), x2))), app(app(filter, app(sub, app(s, app(s, z0)))), x2)), APP(app(sub, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(sub, app(s, app(s, z0)))), x2), APP(app(filter, app(sub, app(s, app(s, z0)))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(sub, app(s, x0)), app(s, x1)), APP(app(filter, app(sub, app(s, x0))), x2), APP(app(filter, app(sub, app(s, x0))), x2)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(sub, app(s, x0))), nil))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(sub, app(s, x0)), app(s, x1))) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(filter, app(sub, app(s, x0))), nil)) APP(app(filter, app(sub, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c4(APP(app(app(if, app(app(sub, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(sub, app(s, x0))), nil))) APP(app(filter, app(gtr, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, false), app(app(cons, app(s, z0)), app(app(filter, app(gtr, app(s, 0))), x2))), app(app(filter, app(gtr, app(s, 0))), x2)), APP(app(gtr, app(s, 0)), app(s, z0)), APP(app(filter, app(gtr, app(s, 0))), x2), APP(app(filter, app(gtr, app(s, 0))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, true), app(app(cons, app(s, 0)), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, app(s, z1))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2))), app(app(filter, app(gtr, app(s, app(s, z0)))), x2)), APP(app(gtr, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2), APP(app(filter, app(gtr, app(s, app(s, z0)))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(gtr, app(s, x0)), app(s, x1)), APP(app(filter, app(gtr, app(s, x0))), x2), APP(app(filter, app(gtr, app(s, x0))), x2)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), app(app(filter, app(gtr, app(s, x0))), nil))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(gtr, app(s, x0)), app(s, x1))) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(filter, app(gtr, app(s, x0))), nil)) APP(app(filter, app(gtr, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c5(APP(app(app(if, app(app(gtr, x0), x1)), app(app(cons, app(s, x1)), nil)), app(app(filter, app(gtr, app(s, x0))), nil))) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, 0), z0)), false), app(app(d, app(s, 0)), z0))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z1)))), app(app(cons, app(s, app(s, z0))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, app(s, z1)), app(s, z0))), false), app(app(d, app(s, app(s, z1))), app(app(sub, z0), z1)))), app(app(cons, app(s, app(s, z0))), app(app(filter, app(d, app(s, app(s, z1)))), x2))), app(app(filter, app(d, app(s, app(s, z1)))), x2)), APP(app(d, app(s, app(s, z1))), app(s, app(s, z0))), APP(app(filter, app(d, app(s, app(s, z1)))), x2), APP(app(filter, app(d, app(s, app(s, z1)))), x2)) APP(app(filter, app(d, app(s, 0))), app(app(cons, app(s, z0)), x2)) -> c38(APP(app(app(if, app(app(app(if, false), false), app(app(d, app(s, 0)), app(app(sub, z0), 0)))), app(app(cons, app(s, z0)), app(app(filter, app(d, app(s, 0))), x2))), app(app(filter, app(d, app(s, 0))), x2)), APP(app(d, app(s, 0)), app(s, z0)), APP(app(filter, app(d, app(s, 0))), x2), APP(app(filter, app(d, app(s, 0))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, 0)), x2)) -> c38(APP(app(app(if, app(app(app(if, true), false), app(app(d, app(s, app(s, z0))), app(app(sub, 0), app(s, z0))))), app(app(cons, app(s, 0)), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, 0)), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, app(s, z0)))), app(app(cons, app(s, app(s, z1))), x2)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, app(s, z0))), app(app(sub, app(s, z1)), app(s, z0))))), app(app(cons, app(s, app(s, z1))), app(app(filter, app(d, app(s, app(s, z0)))), x2))), app(app(filter, app(d, app(s, app(s, z0)))), x2)), APP(app(d, app(s, app(s, z0))), app(s, app(s, z1))), APP(app(filter, app(d, app(s, app(s, z0)))), x2), APP(app(filter, app(d, app(s, app(s, z0)))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), x2)) -> c38(APP(app(filter, app(d, app(s, x0))), x2), APP(app(filter, app(d, app(s, x0))), x2)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), app(app(filter, app(d, app(s, x0))), nil))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(d, app(s, x0)), app(s, x1))) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(filter, app(d, app(s, x0))), nil)) APP(app(filter, app(d, app(s, x0))), app(app(cons, app(s, x1)), nil)) -> c6(APP(app(app(if, app(app(app(if, app(app(gtr, x0), x1)), false), app(app(d, app(s, x0)), app(app(sub, x1), x0)))), app(app(cons, app(s, x1)), nil)), app(app(filter, app(d, app(s, x0))), nil))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), nil))), nil)), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), nil)), app(app(filter, z0), nil))), app(app(cons, app(app(cons, x1), nil)), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), nil)), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c38(APP(app(app(if, app(app(app(if, app(z0, x1)), app(app(cons, x1), app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2)))), app(app(filter, z0), app(app(cons, z1), z2)))), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), app(app(filter, app(filter, z0)), x3))), app(app(filter, app(filter, z0)), x3)), APP(app(filter, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(filter, app(filter, z0)), x3), APP(app(filter, app(filter, z0)), x3)) APP(app(filter, app(filter, app(app(if, true), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, z1), app(app(filter, app(app(if, true), z0)), x2))), app(app(filter, app(app(if, true), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, true), z0))), x3))), app(app(filter, app(filter, app(app(if, true), z0))), x3)), APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, true), z0))), x3), APP(app(filter, app(filter, app(app(if, true), z0))), x3)) APP(app(filter, app(filter, app(app(if, false), z0))), app(app(cons, app(app(cons, z1), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z1), app(app(cons, z1), app(app(filter, app(app(if, false), z0)), x2))), app(app(filter, app(app(if, false), z0)), x2))), app(app(cons, app(app(cons, z1), x2)), app(app(filter, app(filter, app(app(if, false), z0))), x3))), app(app(filter, app(filter, app(app(if, false), z0))), x3)), APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)), APP(app(filter, app(filter, app(app(if, false), z0))), x3), APP(app(filter, app(filter, app(app(if, false), z0))), x3)) APP(app(filter, app(filter, app(sub, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, z0), app(app(cons, 0), app(app(filter, app(sub, z0)), x2))), app(app(filter, app(sub, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(sub, z0))), x3))), app(app(filter, app(filter, app(sub, z0))), x3)), APP(app(filter, app(sub, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(sub, z0))), x3), APP(app(filter, app(filter, app(sub, z0))), x3)) APP(app(filter, app(filter, app(sub, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(sub, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(sub, app(s, z0))), x2))), app(app(filter, app(sub, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(sub, app(s, z0)))), x3))), app(app(filter, app(filter, app(sub, app(s, z0)))), x3)), APP(app(filter, app(sub, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3), APP(app(filter, app(filter, app(sub, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, 0))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, false), app(app(cons, z0), app(app(filter, app(gtr, 0)), x2))), app(app(filter, app(gtr, 0)), x2))), app(app(cons, app(app(cons, z0), x2)), app(app(filter, app(filter, app(gtr, 0))), x3))), app(app(filter, app(filter, app(gtr, 0))), x3)), APP(app(filter, app(gtr, 0)), app(app(cons, z0), x2)), APP(app(filter, app(filter, app(gtr, 0))), x3), APP(app(filter, app(filter, app(gtr, 0))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(gtr, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), app(app(cons, app(s, z1)), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(filter, app(gtr, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3))), app(app(filter, app(filter, app(gtr, app(s, z0)))), x3)), APP(app(filter, app(gtr, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3), APP(app(filter, app(filter, app(gtr, app(s, z0)))), x3)) APP(app(filter, app(filter, app(d, z0))), app(app(cons, app(app(cons, 0), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, true), app(app(cons, 0), app(app(filter, app(d, z0)), x2))), app(app(filter, app(d, z0)), x2))), app(app(cons, app(app(cons, 0), x2)), app(app(filter, app(filter, app(d, z0))), x3))), app(app(filter, app(filter, app(d, z0))), x3)), APP(app(filter, app(d, z0)), app(app(cons, 0), x2)), APP(app(filter, app(filter, app(d, z0))), x3), APP(app(filter, app(filter, app(d, z0))), x3)) APP(app(filter, app(filter, app(d, app(s, z0)))), app(app(cons, app(app(cons, app(s, z1)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(app(gtr, z0), z1)), false), app(app(d, app(s, z0)), app(app(sub, z1), z0)))), app(app(cons, app(s, z1)), app(app(filter, app(d, app(s, z0))), x2))), app(app(filter, app(d, app(s, z0))), x2))), app(app(cons, app(app(cons, app(s, z1)), x2)), app(app(filter, app(filter, app(d, app(s, z0)))), x3))), app(app(filter, app(filter, app(d, app(s, z0)))), x3)), APP(app(filter, app(d, app(s, z0))), app(app(cons, app(s, z1)), x2)), APP(app(filter, app(filter, app(d, app(s, z0)))), x3), APP(app(filter, app(filter, app(d, app(s, z0)))), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c38(APP(app(app(if, app(app(app(if, app(app(app(if, app(z0, z1)), app(app(cons, z1), app(app(filter, z0), z2))), app(app(filter, z0), z2))), app(app(cons, app(app(cons, z1), z2)), app(app(filter, app(filter, z0)), x2))), app(app(filter, app(filter, z0)), x2))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), app(app(filter, app(filter, app(filter, z0))), x3))), app(app(filter, app(filter, app(filter, z0))), x3)), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) APP(app(filter, app(filter, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c38(APP(app(filter, app(filter, x0)), x3), APP(app(filter, app(filter, x0)), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(filter, len), app(app(cons, nil), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, len)), app(app(cons, app(app(cons, app(app(cons, z0), z1)), x2)), x3)) -> c38(APP(app(filter, len), app(app(cons, app(app(cons, z0), z1)), x2)), APP(app(filter, app(filter, len)), x3), APP(app(filter, app(filter, len)), x3)) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c38(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)), APP(app(filter, app(filter, app(filter, z0))), x3), APP(app(filter, app(filter, app(filter, z0))), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c26, c27, c28, c30, c31, c33, c35, c37, c29_1, c32_1, c36_1, c12_1, c1_1, c38_4, c38_3, c_1, c12_3, c12_2, c34_4, c2_1, c3_1, c4_1, c5_1, c38_2, c6_1