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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 260 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 3 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), 59 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 23 ms] (26) CpxRNTS (27) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxRNTS (29) CompletionProof [UPPER BOUND(ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 11 ms] (32) CpxRNTS (33) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (34) CdtProblem (35) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (42) CdtProblem (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 3 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 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), 36 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 89 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 15 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 173 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 62 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 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), 25 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (96) CdtProblem (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 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), 9 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 7 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (124) CdtProblem (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (128) CdtProblem (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) 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: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0), y) -> true a(a(le, a(s, x)), 0) -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), 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(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs ---------------------------------------- (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: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0), y) -> true a(a(le, a(s, x)), 0) -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) The (relative) TRS S consists of the following rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs 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: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0), y) -> true a(a(le, a(s, x)), 0) -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) The (relative) TRS S consists of the following rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs 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: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0), y) -> true a(a(le, a(s, x)), 0) -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) The (relative) TRS S consists of the following rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs 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: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0'), y) -> true a(a(le, a(s, x)), 0') -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) The (relative) TRS S consists of the following rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0') -> 0' encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0' encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0'), y) -> true a(a(le, a(s, x)), 0') -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0') -> 0' encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0' encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs Types: a :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a append :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a nil :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a cons :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a filter :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a if :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a le :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a 0' :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a true :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a s :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a false :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a not :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a not2 :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a qs :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encArg :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a cons_a :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_a :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_append :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_nil :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_cons :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_filter :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_if :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_le :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_0 :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_true :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_s :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_false :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_not :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_not2 :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_qs :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a hole_append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a1_3 :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a gen_append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a2_3 :: Nat -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: a, encArg They will be analysed ascendingly in the following order: a < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0'), y) -> true a(a(le, a(s, x)), 0') -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0') -> 0' encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0' encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs Types: a :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a append :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a nil :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a cons :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a filter :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a if :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a le :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a 0' :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a true :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a s :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a false :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a not :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a not2 :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a qs :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encArg :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a cons_a :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_a :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_append :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_nil :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_cons :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_filter :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_if :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_le :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_0 :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_true :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_s :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_false :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_not :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_not2 :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a encode_qs :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a hole_append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a1_3 :: append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a gen_append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a2_3 :: Nat -> append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a Generator Equations: gen_append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a2_3(0) <=> append gen_append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a2_3(+(x, 1)) <=> cons_a(append, gen_append:nil:cons:filter:if:le:0':true:s:false:not:not2:qs:cons_a2_3(x)) The following defined symbols remain to be analysed: a, encArg They will be analysed ascendingly in the following order: a < 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: a(a(append, nil), ys) -> ys a(a(append, a(a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(le, 0), y) -> true a(a(le, a(s, x)), 0) -> false a(a(le, a(s, x)), a(s, y)) -> a(a(le, x), y) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), b) -> a(not2, a(f, b)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs 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: a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(c_a(filter, f), c_a(c_a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) a(c_a(not, f), b) -> a(not2, a(f, b)) a(c_a(append, nil), ys) -> ys a(c_a(le, c_a(s, x)), 0) -> false a(c_a(le, c_a(s, x)), c_a(s, y)) -> a(a(le, x), y) a(c_a(c_a(if, true), x), xs) -> a(a(cons, x), xs) a(c_a(filter, f), nil) -> nil a(c_a(c_a(if, false), x), xs) -> xs a(c_a(append, c_a(c_a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) a(c_a(le, 0), y) -> true The (relative) TRS S consists of the following rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs a(x0, x1) -> c_a(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: a(not2, true) -> false [1] a(not2, false) -> true [1] a(qs, nil) -> nil [1] a(c_a(filter, f), c_a(c_a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) [1] a(c_a(not, f), b) -> a(not2, a(f, b)) [1] a(c_a(append, nil), ys) -> ys [1] a(c_a(le, c_a(s, x)), 0) -> false [1] a(c_a(le, c_a(s, x)), c_a(s, y)) -> a(a(le, x), y) [1] a(c_a(c_a(if, true), x), xs) -> a(a(cons, x), xs) [1] a(c_a(filter, f), nil) -> nil [1] a(c_a(c_a(if, false), x), xs) -> xs [1] a(c_a(append, c_a(c_a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) [1] a(c_a(le, 0), y) -> true [1] encArg(append) -> append [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(if) -> if [0] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(not) -> not [0] encArg(not2) -> not2 [0] encArg(qs) -> qs [0] encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_append -> append [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_if -> if [0] encode_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_not -> not [0] encode_not2 -> not2 [0] encode_qs -> qs [0] a(x0, x1) -> c_a(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: a(not2, true) -> false [1] a(not2, false) -> true [1] a(qs, nil) -> nil [1] a(c_a(filter, f), c_a(c_a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) [1] a(c_a(not, f), b) -> a(not2, a(f, b)) [1] a(c_a(append, nil), ys) -> ys [1] a(c_a(le, c_a(s, x)), 0) -> false [1] a(c_a(le, c_a(s, x)), c_a(s, y)) -> a(a(le, x), y) [1] a(c_a(c_a(if, true), x), xs) -> a(a(cons, x), xs) [1] a(c_a(filter, f), nil) -> nil [1] a(c_a(c_a(if, false), x), xs) -> xs [1] a(c_a(append, c_a(c_a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) [1] a(c_a(le, 0), y) -> true [1] encArg(append) -> append [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(if) -> if [0] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(not) -> not [0] encArg(not2) -> not2 [0] encArg(qs) -> qs [0] encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_append -> append [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_if -> if [0] encode_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_not -> not [0] encode_not2 -> not2 [0] encode_qs -> qs [0] a(x0, x1) -> c_a(x0, x1) [0] The TRS has the following type information: a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a c_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a 0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encArg :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a cons_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a encode_qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a 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_a_2 encode_append encode_nil encode_cons encode_filter encode_if encode_le encode_0 encode_true encode_s encode_false encode_not encode_not2 encode_qs a_2 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_a(v0, v1) -> null_encode_a [0] encode_append -> null_encode_append [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_if -> null_encode_if [0] encode_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_not -> null_encode_not [0] encode_not2 -> null_encode_not2 [0] encode_qs -> null_encode_qs [0] a(v0, v1) -> null_a [0] And the following fresh constants: null_encArg, null_encode_a, null_encode_append, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_if, null_encode_le, null_encode_0, null_encode_true, null_encode_s, null_encode_false, null_encode_not, null_encode_not2, null_encode_qs, null_a ---------------------------------------- (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: a(not2, true) -> false [1] a(not2, false) -> true [1] a(qs, nil) -> nil [1] a(c_a(filter, f), c_a(c_a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) [1] a(c_a(not, f), b) -> a(not2, a(f, b)) [1] a(c_a(append, nil), ys) -> ys [1] a(c_a(le, c_a(s, x)), 0) -> false [1] a(c_a(le, c_a(s, x)), c_a(s, y)) -> a(a(le, x), y) [1] a(c_a(c_a(if, true), x), xs) -> a(a(cons, x), xs) [1] a(c_a(filter, f), nil) -> nil [1] a(c_a(c_a(if, false), x), xs) -> xs [1] a(c_a(append, c_a(c_a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) [1] a(c_a(le, 0), y) -> true [1] encArg(append) -> append [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(if) -> if [0] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(not) -> not [0] encArg(not2) -> not2 [0] encArg(qs) -> qs [0] encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_append -> append [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_if -> if [0] encode_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_not -> not [0] encode_not2 -> not2 [0] encode_qs -> qs [0] a(x0, x1) -> c_a(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_a(v0, v1) -> null_encode_a [0] encode_append -> null_encode_append [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_if -> null_encode_if [0] encode_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_not -> null_encode_not [0] encode_not2 -> null_encode_not2 [0] encode_qs -> null_encode_qs [0] a(v0, v1) -> null_a [0] The TRS has the following type information: a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a c_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a 0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encArg :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a cons_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encArg :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a 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: a(not2, true) -> false [1] a(not2, false) -> true [1] a(qs, nil) -> nil [1] a(c_a(filter, f), c_a(c_a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, c_a(le, x)), xs))), a(c_a(cons, x), a(qs, a(a(filter, a(not, c_a(le, x))), xs)))) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, c_a(le, x)), xs))), a(c_a(cons, x), a(qs, a(a(filter, a(not, null_a)), xs)))) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, c_a(le, x)), xs))), a(null_a, a(qs, a(a(filter, a(not, c_a(le, x))), xs)))) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, c_a(le, x)), xs))), a(null_a, a(qs, a(a(filter, a(not, null_a)), xs)))) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, null_a), xs))), a(c_a(cons, x), a(qs, a(a(filter, a(not, c_a(le, x))), xs)))) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, null_a), xs))), a(c_a(cons, x), a(qs, a(a(filter, a(not, null_a)), xs)))) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, null_a), xs))), a(null_a, a(qs, a(a(filter, a(not, c_a(le, x))), xs)))) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, null_a), xs))), a(null_a, a(qs, a(a(filter, a(not, null_a)), xs)))) [1] a(c_a(not, not2), true) -> a(not2, false) [2] a(c_a(not, not2), false) -> a(not2, true) [2] a(c_a(not, qs), nil) -> a(not2, nil) [2] a(c_a(not, c_a(filter, f2)), c_a(c_a(cons, x7), xs2)) -> a(not2, a(a(a(if, a(f2, x7)), x7), a(a(filter, f2), xs2))) [2] a(c_a(not, qs), c_a(c_a(cons, x8), xs3)) -> a(not2, a(a(append, a(qs, a(a(filter, a(le, x8)), xs3))), a(a(cons, x8), a(qs, a(a(filter, a(not, a(le, x8))), xs3))))) [2] a(c_a(not, c_a(not, f3)), b) -> a(not2, a(not2, a(f3, b))) [2] a(c_a(not, c_a(append, nil)), b) -> a(not2, b) [2] a(c_a(not, c_a(le, c_a(s, x9))), 0) -> a(not2, false) [2] a(c_a(not, c_a(le, c_a(s, x10))), c_a(s, y'')) -> a(not2, a(a(le, x10), y'')) [2] a(c_a(not, c_a(c_a(if, true), x11)), b) -> a(not2, a(a(cons, x11), b)) [2] a(c_a(not, c_a(filter, f4)), nil) -> a(not2, nil) [2] a(c_a(not, c_a(c_a(if, false), x12)), b) -> a(not2, b) [2] a(c_a(not, c_a(append, c_a(c_a(cons, x13), xs4))), b) -> a(not2, a(a(cons, x13), a(a(append, xs4), b))) [2] a(c_a(not, c_a(le, 0)), b) -> a(not2, true) [2] a(c_a(not, f), b) -> a(not2, c_a(f, b)) [1] a(c_a(not, f), b) -> a(not2, null_a) [1] a(c_a(append, nil), ys) -> ys [1] a(c_a(le, c_a(s, x)), 0) -> false [1] a(c_a(le, c_a(s, x)), c_a(s, y)) -> a(c_a(le, x), y) [1] a(c_a(le, c_a(s, x)), c_a(s, y)) -> a(null_a, y) [1] a(c_a(c_a(if, true), x), xs) -> a(c_a(cons, x), xs) [1] a(c_a(c_a(if, true), x), xs) -> a(null_a, xs) [1] a(c_a(filter, f), nil) -> nil [1] a(c_a(c_a(if, false), x), xs) -> xs [1] a(c_a(append, c_a(c_a(cons, x), xs)), ys) -> a(c_a(cons, x), a(c_a(append, xs), ys)) [1] a(c_a(append, c_a(c_a(cons, x), xs)), ys) -> a(c_a(cons, x), a(null_a, ys)) [1] a(c_a(append, c_a(c_a(cons, x), xs)), ys) -> a(null_a, a(c_a(append, xs), ys)) [1] a(c_a(append, c_a(c_a(cons, x), xs)), ys) -> a(null_a, a(null_a, ys)) [1] a(c_a(le, 0), y) -> true [1] encArg(append) -> append [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(if) -> if [0] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(not) -> not [0] encArg(not2) -> not2 [0] encArg(qs) -> qs [0] encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_append -> append [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_if -> if [0] encode_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_not -> not [0] encode_not2 -> not2 [0] encode_qs -> qs [0] a(x0, x1) -> c_a(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_a(v0, v1) -> null_encode_a [0] encode_append -> null_encode_append [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_if -> null_encode_if [0] encode_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_not -> null_encode_not [0] encode_not2 -> null_encode_not2 [0] encode_qs -> null_encode_qs [0] a(v0, v1) -> null_a [0] The TRS has the following type information: a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a c_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a 0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encArg :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a cons_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encArg :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a 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: not2 => 9 true => 12 false => 3 qs => 10 nil => 7 filter => 4 cons => 2 if => 5 append => 1 le => 6 not => 8 s => 11 0 => 0 null_encArg => 0 null_encode_a => 0 null_encode_append => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_encode_if => 0 null_encode_le => 0 null_encode_0 => 0 null_encode_true => 0 null_encode_s => 0 null_encode_false => 0 null_encode_not => 0 null_encode_not2 => 0 null_encode_qs => 0 null_a => 0 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: a(z, z') -{ 1 }-> xs :|: xs >= 0, x >= 0, z = 1 + (1 + 5 + 3) + x, z' = xs a(z, z') -{ 1 }-> ys :|: z' = ys, ys >= 0, z = 1 + 1 + 7 a(z, z') -{ 1 }-> a(a(a(5, a(f, x)), x), a(a(4, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 4 + f, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 0), xs))), a(0, a(10, a(a(4, a(8, 0)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 0), xs))), a(0, a(10, a(a(4, a(8, 1 + 6 + x)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 0), xs))), a(1 + 2 + x, a(10, a(a(4, a(8, 0)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 0), xs))), a(1 + 2 + x, a(10, a(a(4, a(8, 1 + 6 + x)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 1 + 6 + x), xs))), a(0, a(10, a(a(4, a(8, 0)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 1 + 6 + x), xs))), a(0, a(10, a(a(4, a(8, 1 + 6 + x)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 1 + 6 + x), xs))), a(1 + 2 + x, a(10, a(a(4, a(8, 0)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 1 + 6 + x), xs))), a(1 + 2 + x, a(10, a(a(4, a(8, 1 + 6 + x)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 2 }-> a(9, b) :|: b >= 0, z' = b, z = 1 + 8 + (1 + 1 + 7) a(z, z') -{ 2 }-> a(9, b) :|: b >= 0, x12 >= 0, z' = b, z = 1 + 8 + (1 + (1 + 5 + 3) + x12) a(z, z') -{ 2 }-> a(9, a(a(a(5, a(f2, x7)), x7), a(a(4, f2), xs2))) :|: xs2 >= 0, x7 >= 0, z' = 1 + (1 + 2 + x7) + xs2, z = 1 + 8 + (1 + 4 + f2), f2 >= 0 a(z, z') -{ 2 }-> a(9, a(a(6, x10), y'')) :|: y'' >= 0, z = 1 + 8 + (1 + 6 + (1 + 11 + x10)), x10 >= 0, z' = 1 + 11 + y'' a(z, z') -{ 2 }-> a(9, a(a(2, x11), b)) :|: z = 1 + 8 + (1 + (1 + 5 + 12) + x11), b >= 0, z' = b, x11 >= 0 a(z, z') -{ 2 }-> a(9, a(a(2, x13), a(a(1, xs4), b))) :|: b >= 0, z = 1 + 8 + (1 + 1 + (1 + (1 + 2 + x13) + xs4)), x13 >= 0, z' = b, xs4 >= 0 a(z, z') -{ 2 }-> a(9, a(a(1, a(10, a(a(4, a(6, x8)), xs3))), a(a(2, x8), a(10, a(a(4, a(8, a(6, x8))), xs3))))) :|: z = 1 + 8 + 10, z' = 1 + (1 + 2 + x8) + xs3, x8 >= 0, xs3 >= 0 a(z, z') -{ 2 }-> a(9, a(9, a(f3, b))) :|: b >= 0, z' = b, z = 1 + 8 + (1 + 8 + f3), f3 >= 0 a(z, z') -{ 2 }-> a(9, 7) :|: z = 1 + 8 + 10, z' = 7 a(z, z') -{ 2 }-> a(9, 7) :|: f4 >= 0, z = 1 + 8 + (1 + 4 + f4), z' = 7 a(z, z') -{ 2 }-> a(9, 3) :|: z' = 12, z = 1 + 8 + 9 a(z, z') -{ 2 }-> a(9, 3) :|: z = 1 + 8 + (1 + 6 + (1 + 11 + x9)), x9 >= 0, z' = 0 a(z, z') -{ 2 }-> a(9, 12) :|: z' = 3, z = 1 + 8 + 9 a(z, z') -{ 2 }-> a(9, 12) :|: b >= 0, z' = b, z = 1 + 8 + (1 + 6 + 0) a(z, z') -{ 1 }-> a(9, 0) :|: f >= 0, b >= 0, z = 1 + 8 + f, z' = b a(z, z') -{ 1 }-> a(9, 1 + f + b) :|: f >= 0, b >= 0, z = 1 + 8 + f, z' = b a(z, z') -{ 1 }-> a(0, xs) :|: xs >= 0, x >= 0, z = 1 + (1 + 5 + 12) + x, z' = xs a(z, z') -{ 1 }-> a(0, y) :|: z = 1 + 6 + (1 + 11 + x), x >= 0, y >= 0, z' = 1 + 11 + y a(z, z') -{ 1 }-> a(0, a(0, ys)) :|: xs >= 0, z' = ys, ys >= 0, x >= 0, z = 1 + 1 + (1 + (1 + 2 + x) + xs) a(z, z') -{ 1 }-> a(0, a(1 + 1 + xs, ys)) :|: xs >= 0, z' = ys, ys >= 0, x >= 0, z = 1 + 1 + (1 + (1 + 2 + x) + xs) a(z, z') -{ 1 }-> a(1 + 6 + x, y) :|: z = 1 + 6 + (1 + 11 + x), x >= 0, y >= 0, z' = 1 + 11 + y a(z, z') -{ 1 }-> a(1 + 2 + x, xs) :|: xs >= 0, x >= 0, z = 1 + (1 + 5 + 12) + x, z' = xs a(z, z') -{ 1 }-> a(1 + 2 + x, a(0, ys)) :|: xs >= 0, z' = ys, ys >= 0, x >= 0, z = 1 + 1 + (1 + (1 + 2 + x) + xs) a(z, z') -{ 1 }-> a(1 + 2 + x, a(1 + 1 + xs, ys)) :|: xs >= 0, z' = ys, ys >= 0, x >= 0, z = 1 + 1 + (1 + (1 + 2 + x) + xs) a(z, z') -{ 1 }-> 7 :|: z = 10, z' = 7 a(z, z') -{ 1 }-> 7 :|: f >= 0, z = 1 + 4 + f, z' = 7 a(z, z') -{ 1 }-> 3 :|: z = 9, z' = 12 a(z, z') -{ 1 }-> 3 :|: z = 1 + 6 + (1 + 11 + x), x >= 0, z' = 0 a(z, z') -{ 1 }-> 12 :|: z = 9, z' = 3 a(z, z') -{ 1 }-> 12 :|: y >= 0, z = 1 + 6 + 0, z' = y a(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> a(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 }-> 12 :|: z = 12 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_a(z, z') -{ 0 }-> a(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_a(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_append -{ 0 }-> 1 :|: encode_append -{ 0 }-> 0 :|: encode_cons -{ 0 }-> 2 :|: encode_cons -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_if -{ 0 }-> 5 :|: encode_if -{ 0 }-> 0 :|: encode_le -{ 0 }-> 6 :|: encode_le -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 7 :|: encode_nil -{ 0 }-> 0 :|: encode_not -{ 0 }-> 8 :|: encode_not -{ 0 }-> 0 :|: encode_not2 -{ 0 }-> 9 :|: encode_not2 -{ 0 }-> 0 :|: encode_qs -{ 0 }-> 10 :|: encode_qs -{ 0 }-> 0 :|: encode_s -{ 0 }-> 11 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 12 :|: 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: a(z, z') -{ 1 }-> z' :|: z' >= 0, z = 1 + 1 + 7 a(z, z') -{ 1 }-> z' :|: z' >= 0, z - 10 >= 0 a(z, z') -{ 1 }-> a(a(a(5, a(z - 5, x)), x), a(a(4, z - 5), xs)) :|: z - 5 >= 0, xs >= 0, x >= 0, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 0), xs))), a(0, a(10, a(a(4, a(8, 0)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 0), xs))), a(0, a(10, a(a(4, a(8, 1 + 6 + x)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 0), xs))), a(1 + 2 + x, a(10, a(a(4, a(8, 0)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 0), xs))), a(1 + 2 + x, a(10, a(a(4, a(8, 1 + 6 + x)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 1 + 6 + x), xs))), a(0, a(10, a(a(4, a(8, 0)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 1 + 6 + x), xs))), a(0, a(10, a(a(4, a(8, 1 + 6 + x)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 1 + 6 + x), xs))), a(1 + 2 + x, a(10, a(a(4, a(8, 0)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, 1 + 6 + x), xs))), a(1 + 2 + x, a(10, a(a(4, a(8, 1 + 6 + x)), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 2 }-> a(9, z') :|: z' >= 0, z = 1 + 8 + (1 + 1 + 7) a(z, z') -{ 2 }-> a(9, z') :|: z' >= 0, z - 19 >= 0 a(z, z') -{ 2 }-> a(9, a(a(a(5, a(z - 14, x7)), x7), a(a(4, z - 14), xs2))) :|: xs2 >= 0, x7 >= 0, z' = 1 + (1 + 2 + x7) + xs2, z - 14 >= 0 a(z, z') -{ 2 }-> a(9, a(a(6, z - 28), z' - 12)) :|: z' - 12 >= 0, z - 28 >= 0 a(z, z') -{ 2 }-> a(9, a(a(2, x13), a(a(1, xs4), z'))) :|: z' >= 0, z = 1 + 8 + (1 + 1 + (1 + (1 + 2 + x13) + xs4)), x13 >= 0, xs4 >= 0 a(z, z') -{ 2 }-> a(9, a(a(2, z - 28), z')) :|: z' >= 0, z - 28 >= 0 a(z, z') -{ 2 }-> a(9, a(a(1, a(10, a(a(4, a(6, x8)), xs3))), a(a(2, x8), a(10, a(a(4, a(8, a(6, x8))), xs3))))) :|: z = 1 + 8 + 10, z' = 1 + (1 + 2 + x8) + xs3, x8 >= 0, xs3 >= 0 a(z, z') -{ 2 }-> a(9, a(9, a(z - 18, z'))) :|: z' >= 0, z - 18 >= 0 a(z, z') -{ 2 }-> a(9, 7) :|: z = 1 + 8 + 10, z' = 7 a(z, z') -{ 2 }-> a(9, 7) :|: z - 14 >= 0, z' = 7 a(z, z') -{ 2 }-> a(9, 3) :|: z' = 12, z = 1 + 8 + 9 a(z, z') -{ 2 }-> a(9, 3) :|: z - 28 >= 0, z' = 0 a(z, z') -{ 2 }-> a(9, 12) :|: z' = 3, z = 1 + 8 + 9 a(z, z') -{ 2 }-> a(9, 12) :|: z' >= 0, z = 1 + 8 + (1 + 6 + 0) a(z, z') -{ 1 }-> a(9, 0) :|: z - 9 >= 0, z' >= 0 a(z, z') -{ 1 }-> a(9, 1 + (z - 9) + z') :|: z - 9 >= 0, z' >= 0 a(z, z') -{ 1 }-> a(0, z') :|: z' >= 0, z - 19 >= 0 a(z, z') -{ 1 }-> a(0, a(0, z')) :|: xs >= 0, z' >= 0, x >= 0, z = 1 + 1 + (1 + (1 + 2 + x) + xs) a(z, z') -{ 1 }-> a(0, a(1 + 1 + xs, z')) :|: xs >= 0, z' >= 0, x >= 0, z = 1 + 1 + (1 + (1 + 2 + x) + xs) a(z, z') -{ 1 }-> a(0, z' - 12) :|: z - 19 >= 0, z' - 12 >= 0 a(z, z') -{ 1 }-> a(1 + 6 + (z - 19), z' - 12) :|: z - 19 >= 0, z' - 12 >= 0 a(z, z') -{ 1 }-> a(1 + 2 + x, a(0, z')) :|: xs >= 0, z' >= 0, x >= 0, z = 1 + 1 + (1 + (1 + 2 + x) + xs) a(z, z') -{ 1 }-> a(1 + 2 + x, a(1 + 1 + xs, z')) :|: xs >= 0, z' >= 0, x >= 0, z = 1 + 1 + (1 + (1 + 2 + x) + xs) a(z, z') -{ 1 }-> a(1 + 2 + (z - 19), z') :|: z' >= 0, z - 19 >= 0 a(z, z') -{ 1 }-> 7 :|: z = 10, z' = 7 a(z, z') -{ 1 }-> 7 :|: z - 5 >= 0, z' = 7 a(z, z') -{ 1 }-> 3 :|: z = 9, z' = 12 a(z, z') -{ 1 }-> 3 :|: z - 19 >= 0, z' = 0 a(z, z') -{ 1 }-> 12 :|: z = 9, z' = 3 a(z, z') -{ 1 }-> 12 :|: z' >= 0, z = 1 + 6 + 0 a(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 encArg(z) -{ 0 }-> a(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 }-> 12 :|: z = 12 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_a(z, z') -{ 0 }-> a(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_a(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_append -{ 0 }-> 1 :|: encode_append -{ 0 }-> 0 :|: encode_cons -{ 0 }-> 2 :|: encode_cons -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_if -{ 0 }-> 5 :|: encode_if -{ 0 }-> 0 :|: encode_le -{ 0 }-> 6 :|: encode_le -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 7 :|: encode_nil -{ 0 }-> 0 :|: encode_not -{ 0 }-> 8 :|: encode_not -{ 0 }-> 0 :|: encode_not2 -{ 0 }-> 9 :|: encode_not2 -{ 0 }-> 0 :|: encode_qs -{ 0 }-> 10 :|: encode_qs -{ 0 }-> 0 :|: encode_s -{ 0 }-> 11 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 12 :|: 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_a(v0, v1) -> null_encode_a [0] encode_append -> null_encode_append [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_if -> null_encode_if [0] encode_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_not -> null_encode_not [0] encode_not2 -> null_encode_not2 [0] encode_qs -> null_encode_qs [0] a(v0, v1) -> null_a [0] And the following fresh constants: null_encArg, null_encode_a, null_encode_append, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_if, null_encode_le, null_encode_0, null_encode_true, null_encode_s, null_encode_false, null_encode_not, null_encode_not2, null_encode_qs, null_a ---------------------------------------- (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: a(not2, true) -> false [1] a(not2, false) -> true [1] a(qs, nil) -> nil [1] a(c_a(filter, f), c_a(c_a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) [1] a(qs, c_a(c_a(cons, x), xs)) -> a(a(append, a(qs, a(a(filter, a(le, x)), xs))), a(a(cons, x), a(qs, a(a(filter, a(not, a(le, x))), xs)))) [1] a(c_a(not, f), b) -> a(not2, a(f, b)) [1] a(c_a(append, nil), ys) -> ys [1] a(c_a(le, c_a(s, x)), 0) -> false [1] a(c_a(le, c_a(s, x)), c_a(s, y)) -> a(a(le, x), y) [1] a(c_a(c_a(if, true), x), xs) -> a(a(cons, x), xs) [1] a(c_a(filter, f), nil) -> nil [1] a(c_a(c_a(if, false), x), xs) -> xs [1] a(c_a(append, c_a(c_a(cons, x), xs)), ys) -> a(a(cons, x), a(a(append, xs), ys)) [1] a(c_a(le, 0), y) -> true [1] encArg(append) -> append [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(if) -> if [0] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(not) -> not [0] encArg(not2) -> not2 [0] encArg(qs) -> qs [0] encArg(cons_a(x_1, x_2)) -> a(encArg(x_1), encArg(x_2)) [0] encode_a(x_1, x_2) -> a(encArg(x_1), encArg(x_2)) [0] encode_append -> append [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_if -> if [0] encode_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_not -> not [0] encode_not2 -> not2 [0] encode_qs -> qs [0] a(x0, x1) -> c_a(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_a(v0, v1) -> null_encode_a [0] encode_append -> null_encode_append [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_if -> null_encode_if [0] encode_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_not -> null_encode_not [0] encode_not2 -> null_encode_not2 [0] encode_qs -> null_encode_qs [0] a(v0, v1) -> null_a [0] The TRS has the following type information: a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a c_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a 0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encArg :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a cons_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a -> not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a encode_qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encArg :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_append :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_nil :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_cons :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_filter :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_if :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_le :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_0 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_true :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_s :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_false :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_not :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_not2 :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_encode_qs :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a null_a :: not2:true:false:qs:nil:filter:c_a:cons:if:append:le:not:s:0:cons_a:null_encArg:null_encode_a:null_encode_append:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_if:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_not:null_encode_not2:null_encode_qs:null_a 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: not2 => 9 true => 12 false => 3 qs => 10 nil => 7 filter => 4 cons => 2 if => 5 append => 1 le => 6 not => 8 s => 11 0 => 0 null_encArg => 0 null_encode_a => 0 null_encode_append => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_encode_if => 0 null_encode_le => 0 null_encode_0 => 0 null_encode_true => 0 null_encode_s => 0 null_encode_false => 0 null_encode_not => 0 null_encode_not2 => 0 null_encode_qs => 0 null_a => 0 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: a(z, z') -{ 1 }-> xs :|: xs >= 0, x >= 0, z = 1 + (1 + 5 + 3) + x, z' = xs a(z, z') -{ 1 }-> ys :|: z' = ys, ys >= 0, z = 1 + 1 + 7 a(z, z') -{ 1 }-> a(a(a(5, a(f, x)), x), a(a(4, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z = 1 + 4 + f, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(a(6, x), y) :|: z = 1 + 6 + (1 + 11 + x), x >= 0, y >= 0, z' = 1 + 11 + y a(z, z') -{ 1 }-> a(a(2, x), xs) :|: xs >= 0, x >= 0, z = 1 + (1 + 5 + 12) + x, z' = xs a(z, z') -{ 1 }-> a(a(2, x), a(a(1, xs), ys)) :|: xs >= 0, z' = ys, ys >= 0, x >= 0, z = 1 + 1 + (1 + (1 + 2 + x) + xs) a(z, z') -{ 1 }-> a(a(1, a(10, a(a(4, a(6, x)), xs))), a(a(2, x), a(10, a(a(4, a(8, a(6, x))), xs)))) :|: xs >= 0, x >= 0, z = 10, z' = 1 + (1 + 2 + x) + xs a(z, z') -{ 1 }-> a(9, a(f, b)) :|: f >= 0, b >= 0, z = 1 + 8 + f, z' = b a(z, z') -{ 1 }-> 7 :|: z = 10, z' = 7 a(z, z') -{ 1 }-> 7 :|: f >= 0, z = 1 + 4 + f, z' = 7 a(z, z') -{ 1 }-> 3 :|: z = 9, z' = 12 a(z, z') -{ 1 }-> 3 :|: z = 1 + 6 + (1 + 11 + x), x >= 0, z' = 0 a(z, z') -{ 1 }-> 12 :|: z = 9, z' = 3 a(z, z') -{ 1 }-> 12 :|: y >= 0, z = 1 + 6 + 0, z' = y a(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> a(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 }-> 12 :|: z = 12 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_a(z, z') -{ 0 }-> a(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_a(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_append -{ 0 }-> 1 :|: encode_append -{ 0 }-> 0 :|: encode_cons -{ 0 }-> 2 :|: encode_cons -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_if -{ 0 }-> 5 :|: encode_if -{ 0 }-> 0 :|: encode_le -{ 0 }-> 6 :|: encode_le -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 7 :|: encode_nil -{ 0 }-> 0 :|: encode_not -{ 0 }-> 8 :|: encode_not -{ 0 }-> 0 :|: encode_not2 -{ 0 }-> 9 :|: encode_not2 -{ 0 }-> 0 :|: encode_qs -{ 0 }-> 10 :|: encode_qs -{ 0 }-> 0 :|: encode_s -{ 0 }-> 11 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 12 :|: 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(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: ENCARG(append) -> c ENCARG(nil) -> c1 ENCARG(cons) -> c2 ENCARG(filter) -> c3 ENCARG(if) -> c4 ENCARG(le) -> c5 ENCARG(0) -> c6 ENCARG(true) -> c7 ENCARG(s) -> c8 ENCARG(false) -> c9 ENCARG(not) -> c10 ENCARG(not2) -> c11 ENCARG(qs) -> c12 ENCARG(cons_a(z0, z1)) -> c13(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_A(z0, z1) -> c14(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APPEND -> c15 ENCODE_NIL -> c16 ENCODE_CONS -> c17 ENCODE_FILTER -> c18 ENCODE_IF -> c19 ENCODE_LE -> c20 ENCODE_0 -> c21 ENCODE_TRUE -> c22 ENCODE_S -> c23 ENCODE_FALSE -> c24 ENCODE_NOT -> c25 ENCODE_NOT2 -> c26 ENCODE_QS -> c27 A(a(append, nil), z0) -> c28 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(cons, z0), a(a(append, z1), z2)), A(cons, z0), A(a(append, z1), z2), A(append, z1)) A(a(filter, z0), nil) -> c30 A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(a(if, a(z0, z1)), z1), A(if, a(z0, z1)), A(z0, z1), A(a(filter, z0), z2), A(filter, z0)) A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1), A(le, z0)) A(a(a(if, true), z0), z1) -> c35(A(a(cons, z0), z1), A(cons, z0)) A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(append, a(qs, a(a(filter, a(le, z0)), z1))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(filter, a(le, z0)), A(le, z0), A(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))), A(cons, z0), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1), A(filter, a(not, a(le, z0))), A(not, a(le, z0)), A(le, z0)) S tuples: A(a(append, nil), z0) -> c28 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(cons, z0), a(a(append, z1), z2)), A(cons, z0), A(a(append, z1), z2), A(append, z1)) A(a(filter, z0), nil) -> c30 A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(a(if, a(z0, z1)), z1), A(if, a(z0, z1)), A(z0, z1), A(a(filter, z0), z2), A(filter, z0)) A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1), A(le, z0)) A(a(a(if, true), z0), z1) -> c35(A(a(cons, z0), z1), A(cons, z0)) A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(append, a(qs, a(a(filter, a(le, z0)), z1))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(filter, a(le, z0)), A(le, z0), A(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))), A(cons, z0), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1), A(filter, a(not, a(le, z0))), A(not, a(le, z0)), A(le, z0)) K tuples:none Defined Rule Symbols: a_2, encArg_1, encode_a_2, encode_append, encode_nil, encode_cons, encode_filter, encode_if, encode_le, encode_0, encode_true, encode_s, encode_false, encode_not, encode_not2, encode_qs Defined Pair Symbols: ENCARG_1, ENCODE_A_2, ENCODE_APPEND, ENCODE_NIL, ENCODE_CONS, ENCODE_FILTER, ENCODE_IF, ENCODE_LE, ENCODE_0, ENCODE_TRUE, ENCODE_S, ENCODE_FALSE, ENCODE_NOT, ENCODE_NOT2, ENCODE_QS, A_2 Compound Symbols: c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13_3, c14_3, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29_4, c30, c31_6, c32, c33, c34_2, c35_2, c36, c37_2, c38, c39, c40, c41_13 ---------------------------------------- (35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 26 trailing nodes: ENCARG(filter) -> c3 ENCODE_IF -> c19 ENCODE_S -> c23 ENCARG(false) -> c9 ENCARG(not2) -> c11 ENCODE_QS -> c27 ENCODE_0 -> c21 ENCARG(not) -> c10 ENCODE_CONS -> c17 ENCARG(nil) -> c1 ENCARG(if) -> c4 ENCODE_NIL -> c16 ENCODE_APPEND -> c15 ENCODE_NOT -> c25 ENCODE_LE -> c20 ENCODE_FALSE -> c24 ENCODE_TRUE -> c22 ENCARG(s) -> c8 ENCARG(0) -> c6 ENCODE_FILTER -> c18 ENCARG(qs) -> c12 ENCARG(cons) -> c2 ENCARG(true) -> c7 ENCARG(le) -> c5 ENCODE_NOT2 -> c26 ENCARG(append) -> c ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: ENCARG(cons_a(z0, z1)) -> c13(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_A(z0, z1) -> c14(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) A(a(append, nil), z0) -> c28 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(cons, z0), a(a(append, z1), z2)), A(cons, z0), A(a(append, z1), z2), A(append, z1)) A(a(filter, z0), nil) -> c30 A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(a(if, a(z0, z1)), z1), A(if, a(z0, z1)), A(z0, z1), A(a(filter, z0), z2), A(filter, z0)) A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1), A(le, z0)) A(a(a(if, true), z0), z1) -> c35(A(a(cons, z0), z1), A(cons, z0)) A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(append, a(qs, a(a(filter, a(le, z0)), z1))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(filter, a(le, z0)), A(le, z0), A(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))), A(cons, z0), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1), A(filter, a(not, a(le, z0))), A(not, a(le, z0)), A(le, z0)) S tuples: A(a(append, nil), z0) -> c28 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(cons, z0), a(a(append, z1), z2)), A(cons, z0), A(a(append, z1), z2), A(append, z1)) A(a(filter, z0), nil) -> c30 A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(a(if, a(z0, z1)), z1), A(if, a(z0, z1)), A(z0, z1), A(a(filter, z0), z2), A(filter, z0)) A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1), A(le, z0)) A(a(a(if, true), z0), z1) -> c35(A(a(cons, z0), z1), A(cons, z0)) A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(append, a(qs, a(a(filter, a(le, z0)), z1))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(filter, a(le, z0)), A(le, z0), A(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))), A(cons, z0), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1), A(filter, a(not, a(le, z0))), A(not, a(le, z0)), A(le, z0)) K tuples:none Defined Rule Symbols: a_2, encArg_1, encode_a_2, encode_append, encode_nil, encode_cons, encode_filter, encode_if, encode_le, encode_0, encode_true, encode_s, encode_false, encode_not, encode_not2, encode_qs Defined Pair Symbols: ENCARG_1, ENCODE_A_2, A_2 Compound Symbols: c13_3, c14_3, c28, c29_4, c30, c31_6, c32, c33, c34_2, c35_2, c36, c37_2, c38, c39, c40, c41_13 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 17 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: ENCARG(cons_a(z0, z1)) -> c13(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_A(z0, z1) -> c14(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) K tuples:none Defined Rule Symbols: a_2, encArg_1, encode_a_2, encode_append, encode_nil, encode_cons, encode_filter, encode_if, encode_le, encode_0, encode_true, encode_s, encode_false, encode_not, encode_not2, encode_qs Defined Pair Symbols: ENCARG_1, ENCODE_A_2, A_2 Compound Symbols: c13_3, c14_3, c28, c30, c32, c33, c36, c37_2, c38, c39, c40, c29_1, c31_3, c34_1, c35, c41_5 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: ENCARG(cons_a(z0, z1)) -> c13(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) ENCODE_A(z0, z1) -> c(ENCARG(z0)) ENCODE_A(z0, z1) -> c(ENCARG(z1)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) K tuples:none Defined Rule Symbols: a_2, encArg_1, encode_a_2, encode_append, encode_nil, encode_cons, encode_filter, encode_if, encode_le, encode_0, encode_true, encode_s, encode_false, encode_not, encode_not2, encode_qs Defined Pair Symbols: ENCARG_1, A_2, ENCODE_A_2 Compound Symbols: c13_3, c28, c30, c32, c33, c36, c37_2, c38, c39, c40, c29_1, c31_3, c34_1, c35, c41_5, c_1 ---------------------------------------- (41) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_A(z0, z1) -> c(ENCARG(z0)) ENCODE_A(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: ENCARG(cons_a(z0, z1)) -> c13(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) K tuples:none Defined Rule Symbols: a_2, encArg_1, encode_a_2, encode_append, encode_nil, encode_cons, encode_filter, encode_if, encode_le, encode_0, encode_true, encode_s, encode_false, encode_not, encode_not2, encode_qs Defined Pair Symbols: ENCARG_1, A_2, ENCODE_A_2 Compound Symbols: c13_3, c28, c30, c32, c33, c36, c37_2, c38, c39, c40, c29_1, c31_3, c34_1, c35, c41_5, c_1 ---------------------------------------- (43) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_a(z0, z1) -> a(encArg(z0), encArg(z1)) encode_append -> append encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_if -> if encode_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_not -> not encode_not2 -> not2 encode_qs -> qs ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: ENCARG(cons_a(z0, z1)) -> c13(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: ENCARG_1, A_2, ENCODE_A_2 Compound Symbols: c13_3, c28, c30, c32, c33, c36, c37_2, c38, c39, c40, c29_1, c31_3, c34_1, c35, c41_5, c_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(z0, z1)) -> c13(A(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0), ENCARG(append)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0), ENCARG(if)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0), ENCARG(le)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0), ENCARG(not)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0), ENCARG(not2)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0), ENCARG(qs)) ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(append, x1)) -> c13(A(append, encArg(x1)), ENCARG(append), ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(A(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(A(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(A(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(A(if, encArg(x1)), ENCARG(if), ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(A(le, encArg(x1)), ENCARG(le), ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(A(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(A(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(A(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(A(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(A(not, encArg(x1)), ENCARG(not), ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(not2), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(qs), ENCARG(x1)) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0), ENCARG(append)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0), ENCARG(if)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0), ENCARG(le)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0), ENCARG(not)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0), ENCARG(not2)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0), ENCARG(qs)) ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(append, x1)) -> c13(A(append, encArg(x1)), ENCARG(append), ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(A(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(A(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(A(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(A(if, encArg(x1)), ENCARG(if), ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(A(le, encArg(x1)), ENCARG(le), ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(A(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(A(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(A(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(A(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(A(not, encArg(x1)), ENCARG(not), ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(not2), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(qs), ENCARG(x1)) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCODE_A_2, ENCARG_1 Compound Symbols: c28, c30, c32, c33, c36, c37_2, c38, c39, c40, c29_1, c31_3, c34_1, c35, c41_5, c_1, c13_3 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 37 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCODE_A_2, ENCARG_1 Compound Symbols: c28, c30, c32, c33, c36, c37_2, c38, c39, c40, c29_1, c31_3, c34_1, c35, c41_5, c_1, c13_3, c13_2, c13_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A(a(not, z0), z1) -> c37(A(not2, a(z0, z1)), A(z0, z1)) by A(a(not, a(append, nil)), z0) -> c37(A(not2, z0), A(a(append, nil), z0)) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(not2, a(a(cons, z0), a(a(append, z1), z2))), A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(not2, nil), A(a(filter, z0), nil)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(le, 0)), z0) -> c37(A(not2, true), A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c37(A(not2, false), A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c37(A(not2, a(a(le, z0), z1)), A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, true), z0)), z1) -> c37(A(not2, a(a(cons, z0), z1)), A(a(a(if, true), z0), z1)) A(a(not, a(a(if, false), z0)), z1) -> c37(A(not2, z1), A(a(a(if, false), z0), z1)) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, not2), true) -> c37(A(not2, false), A(not2, true)) A(a(not, not2), false) -> c37(A(not2, true), A(not2, false)) A(a(not, qs), nil) -> c37(A(not2, nil), A(qs, nil)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(append, nil)), z0) -> c37(A(not2, z0), A(a(append, nil), z0)) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(not2, a(a(cons, z0), a(a(append, z1), z2))), A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(not2, nil), A(a(filter, z0), nil)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(le, 0)), z0) -> c37(A(not2, true), A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c37(A(not2, false), A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c37(A(not2, a(a(le, z0), z1)), A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, true), z0)), z1) -> c37(A(not2, a(a(cons, z0), z1)), A(a(a(if, true), z0), z1)) A(a(not, a(a(if, false), z0)), z1) -> c37(A(not2, z1), A(a(a(if, false), z0), z1)) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, not2), true) -> c37(A(not2, false), A(not2, true)) A(a(not, not2), false) -> c37(A(not2, true), A(not2, false)) A(a(not, qs), nil) -> c37(A(not2, nil), A(qs, nil)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) A(a(not, a(append, nil)), z0) -> c37(A(not2, z0), A(a(append, nil), z0)) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(not2, a(a(cons, z0), a(a(append, z1), z2))), A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(not2, nil), A(a(filter, z0), nil)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(le, 0)), z0) -> c37(A(not2, true), A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c37(A(not2, false), A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c37(A(not2, a(a(le, z0), z1)), A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, true), z0)), z1) -> c37(A(not2, a(a(cons, z0), z1)), A(a(a(if, true), z0), z1)) A(a(not, a(a(if, false), z0)), z1) -> c37(A(not2, z1), A(a(a(if, false), z0), z1)) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, not2), true) -> c37(A(not2, false), A(not2, true)) A(a(not, not2), false) -> c37(A(not2, true), A(not2, false)) A(a(not, qs), nil) -> c37(A(not2, nil), A(qs, nil)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCODE_A_2, ENCARG_1 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c31_3, c34_1, c35, c41_5, c_1, c13_3, c13_2, c13_1, c37_2 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(append, nil)), z0) -> c37(A(not2, z0), A(a(append, nil), z0)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(le, 0)), z0) -> c37(A(not2, true), A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c37(A(not2, false), A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c37(A(not2, a(a(le, z0), z1)), A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c37(A(not2, z1), A(a(a(if, false), z0), z1)) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, not2), true) -> c37(A(not2, false), A(not2, true)) A(a(not, not2), false) -> c37(A(not2, true), A(not2, false)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) A(a(not, a(append, nil)), z0) -> c37(A(not2, z0), A(a(append, nil), z0)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(le, 0)), z0) -> c37(A(not2, true), A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c37(A(not2, false), A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c37(A(not2, a(a(le, z0), z1)), A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c37(A(not2, z1), A(a(a(if, false), z0), z1)) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, not2), true) -> c37(A(not2, false), A(not2, true)) A(a(not, not2), false) -> c37(A(not2, true), A(not2, false)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCODE_A_2, ENCARG_1 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c31_3, c34_1, c35, c41_5, c_1, c13_3, c13_2, c13_1, c37_2, c37_1 ---------------------------------------- (53) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCODE_A_2, ENCARG_1 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c31_3, c34_1, c35, c41_5, c_1, c13_3, c13_2, c13_1, c37_2, c37_1, c1_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A(a(filter, z0), a(a(cons, z1), z2)) -> c31(A(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)), A(z0, z1), A(a(filter, z0), z2)) by A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(a(if, a(a(cons, z0), a(a(append, z1), z2))), z2), a(a(filter, a(append, a(a(cons, z0), z1))), x2)), A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(a(if, nil), nil), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(a(cons, z0), z1)), z1), a(a(filter, a(a(if, true), z0)), x2)), A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(a(a(if, nil), nil), a(a(filter, qs), x2)), A(qs, nil), A(a(filter, qs), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(a(if, a(a(cons, z0), a(a(append, z1), z2))), z2), a(a(filter, a(append, a(a(cons, z0), z1))), x2)), A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(a(if, nil), nil), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(a(cons, z0), z1)), z1), a(a(filter, a(a(if, true), z0)), x2)), A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(a(a(if, nil), nil), a(a(filter, qs), x2)), A(qs, nil), A(a(filter, qs), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(a(if, a(a(cons, z0), a(a(append, z1), z2))), z2), a(a(filter, a(append, a(a(cons, z0), z1))), x2)), A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(a(if, nil), nil), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(a(cons, z0), z1)), z1), a(a(filter, a(a(if, true), z0)), x2)), A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(a(a(if, nil), nil), a(a(filter, qs), x2)), A(qs, nil), A(a(filter, qs), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCODE_A_2, ENCARG_1 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c41_5, c_1, c13_3, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCODE_A_2, ENCARG_1 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c41_5, c_1, c13_3, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A(qs, a(a(cons, z0), z1)) -> c41(A(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))), A(qs, a(a(filter, a(le, z0)), z1)), A(a(filter, a(le, z0)), z1), A(qs, a(a(filter, a(not, a(le, z0))), z1)), A(a(filter, a(not, a(le, z0))), z1)) by A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCODE_A_2, ENCARG_1 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c_1, c13_3, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_A(z0, z1) -> c(A(encArg(z0), encArg(z1))) by ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(append, x1) -> c(A(append, encArg(x1))) ENCODE_A(nil, x1) -> c(A(nil, encArg(x1))) ENCODE_A(cons, x1) -> c(A(cons, encArg(x1))) ENCODE_A(filter, x1) -> c(A(filter, encArg(x1))) ENCODE_A(if, x1) -> c(A(if, encArg(x1))) ENCODE_A(le, x1) -> c(A(le, encArg(x1))) ENCODE_A(0, x1) -> c(A(0, encArg(x1))) ENCODE_A(true, x1) -> c(A(true, encArg(x1))) ENCODE_A(s, x1) -> c(A(s, encArg(x1))) ENCODE_A(false, x1) -> c(A(false, encArg(x1))) ENCODE_A(not, x1) -> c(A(not, encArg(x1))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(append, x1) -> c(A(append, encArg(x1))) ENCODE_A(nil, x1) -> c(A(nil, encArg(x1))) ENCODE_A(cons, x1) -> c(A(cons, encArg(x1))) ENCODE_A(filter, x1) -> c(A(filter, encArg(x1))) ENCODE_A(if, x1) -> c(A(if, encArg(x1))) ENCODE_A(le, x1) -> c(A(le, encArg(x1))) ENCODE_A(0, x1) -> c(A(0, encArg(x1))) ENCODE_A(true, x1) -> c(A(true, encArg(x1))) ENCODE_A(s, x1) -> c(A(s, encArg(x1))) ENCODE_A(false, x1) -> c(A(false, encArg(x1))) ENCODE_A(not, x1) -> c(A(not, encArg(x1))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_3, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 11 trailing nodes: ENCODE_A(if, x1) -> c(A(if, encArg(x1))) ENCODE_A(not, x1) -> c(A(not, encArg(x1))) ENCODE_A(le, x1) -> c(A(le, encArg(x1))) ENCODE_A(append, x1) -> c(A(append, encArg(x1))) ENCODE_A(nil, x1) -> c(A(nil, encArg(x1))) ENCODE_A(0, x1) -> c(A(0, encArg(x1))) ENCODE_A(cons, x1) -> c(A(cons, encArg(x1))) ENCODE_A(filter, x1) -> c(A(filter, encArg(x1))) ENCODE_A(s, x1) -> c(A(s, encArg(x1))) ENCODE_A(true, x1) -> c(A(true, encArg(x1))) ENCODE_A(false, x1) -> c(A(false, encArg(x1))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_3, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, cons_a(z0, z1))) -> c13(A(encArg(x0), a(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_a(z0, z1))) by ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(A(append, a(encArg(x1), encArg(x2))), ENCARG(append), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(A(nil, a(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(A(cons, a(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(A(filter, a(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(A(if, a(encArg(x1), encArg(x2))), ENCARG(if), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(A(le, a(encArg(x1), encArg(x2))), ENCARG(le), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(A(0, a(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(A(true, a(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(A(s, a(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(A(false, a(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(A(not, a(encArg(x1), encArg(x2))), ENCARG(not), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(not2), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(qs), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(A(append, a(encArg(x1), encArg(x2))), ENCARG(append), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(A(nil, a(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(A(cons, a(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(A(filter, a(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(A(if, a(encArg(x1), encArg(x2))), ENCARG(if), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(A(le, a(encArg(x1), encArg(x2))), ENCARG(le), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(A(0, a(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(A(true, a(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(A(s, a(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(A(false, a(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(A(not, a(encArg(x1), encArg(x2))), ENCARG(not), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(not2), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(qs), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_3, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 24 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_3, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(cons_a(z0, z1), x1)) -> c13(A(a(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_a(z0, z1)), ENCARG(x1)) by ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1)), ENCARG(append)) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1)), ENCARG(nil)) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1)), ENCARG(cons)) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1)), ENCARG(filter)) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1)), ENCARG(if)) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1)), ENCARG(le)) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1)), ENCARG(0)) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1)), ENCARG(true)) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1)), ENCARG(s)) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1)), ENCARG(false)) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1)), ENCARG(not)) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1)), ENCARG(not2)) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1)), ENCARG(qs)) ENCARG(cons_a(cons_a(x0, x1), cons_a(z0, z1))) -> c13(A(a(encArg(x0), encArg(x1)), a(encArg(z0), encArg(z1))), ENCARG(cons_a(x0, x1)), ENCARG(cons_a(z0, z1))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(A(a(nil, encArg(x1)), encArg(x2)), ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(A(a(cons, encArg(x1)), encArg(x2)), ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(A(a(if, encArg(x1)), encArg(x2)), ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(A(a(0, encArg(x1)), encArg(x2)), ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(A(a(true, encArg(x1)), encArg(x2)), ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(A(a(s, encArg(x1)), encArg(x2)), ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(A(a(false, encArg(x1)), encArg(x2)), ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1)), ENCARG(append)) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1)), ENCARG(nil)) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1)), ENCARG(cons)) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1)), ENCARG(filter)) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1)), ENCARG(if)) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1)), ENCARG(le)) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1)), ENCARG(0)) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1)), ENCARG(true)) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1)), ENCARG(s)) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1)), ENCARG(false)) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1)), ENCARG(not)) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1)), ENCARG(not2)) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1)), ENCARG(qs)) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(A(a(nil, encArg(x1)), encArg(x2)), ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(A(a(cons, encArg(x1)), encArg(x2)), ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(A(a(if, encArg(x1)), encArg(x2)), ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(A(a(0, encArg(x1)), encArg(x2)), ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(A(a(true, encArg(x1)), encArg(x2)), ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(A(a(s, encArg(x1)), encArg(x2)), ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(A(a(false, encArg(x1)), encArg(x2)), ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, append)) -> c13(A(encArg(x0), append), ENCARG(x0)) by ENCARG(cons_a(append, append)) -> c13(A(append, append), ENCARG(append)) ENCARG(cons_a(nil, append)) -> c13(A(nil, append), ENCARG(nil)) ENCARG(cons_a(cons, append)) -> c13(A(cons, append), ENCARG(cons)) ENCARG(cons_a(filter, append)) -> c13(A(filter, append), ENCARG(filter)) ENCARG(cons_a(if, append)) -> c13(A(if, append), ENCARG(if)) ENCARG(cons_a(le, append)) -> c13(A(le, append), ENCARG(le)) ENCARG(cons_a(0, append)) -> c13(A(0, append), ENCARG(0)) ENCARG(cons_a(true, append)) -> c13(A(true, append), ENCARG(true)) ENCARG(cons_a(s, append)) -> c13(A(s, append), ENCARG(s)) ENCARG(cons_a(false, append)) -> c13(A(false, append), ENCARG(false)) ENCARG(cons_a(not, append)) -> c13(A(not, append), ENCARG(not)) ENCARG(cons_a(not2, append)) -> c13(A(not2, append), ENCARG(not2)) ENCARG(cons_a(qs, append)) -> c13(A(qs, append), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), append)) -> c13(A(a(encArg(z0), encArg(z1)), append), ENCARG(cons_a(z0, z1))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(append, append)) -> c13(A(append, append), ENCARG(append)) ENCARG(cons_a(nil, append)) -> c13(A(nil, append), ENCARG(nil)) ENCARG(cons_a(cons, append)) -> c13(A(cons, append), ENCARG(cons)) ENCARG(cons_a(filter, append)) -> c13(A(filter, append), ENCARG(filter)) ENCARG(cons_a(if, append)) -> c13(A(if, append), ENCARG(if)) ENCARG(cons_a(le, append)) -> c13(A(le, append), ENCARG(le)) ENCARG(cons_a(0, append)) -> c13(A(0, append), ENCARG(0)) ENCARG(cons_a(true, append)) -> c13(A(true, append), ENCARG(true)) ENCARG(cons_a(s, append)) -> c13(A(s, append), ENCARG(s)) ENCARG(cons_a(false, append)) -> c13(A(false, append), ENCARG(false)) ENCARG(cons_a(not, append)) -> c13(A(not, append), ENCARG(not)) ENCARG(cons_a(not2, append)) -> c13(A(not2, append), ENCARG(not2)) ENCARG(cons_a(qs, append)) -> c13(A(qs, append), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(s, append)) -> c13(A(s, append), ENCARG(s)) ENCARG(cons_a(not2, append)) -> c13(A(not2, append), ENCARG(not2)) ENCARG(cons_a(true, append)) -> c13(A(true, append), ENCARG(true)) ENCARG(cons_a(filter, append)) -> c13(A(filter, append), ENCARG(filter)) ENCARG(cons_a(if, append)) -> c13(A(if, append), ENCARG(if)) ENCARG(cons_a(nil, append)) -> c13(A(nil, append), ENCARG(nil)) ENCARG(cons_a(append, append)) -> c13(A(append, append), ENCARG(append)) ENCARG(cons_a(qs, append)) -> c13(A(qs, append), ENCARG(qs)) ENCARG(cons_a(0, append)) -> c13(A(0, append), ENCARG(0)) ENCARG(cons_a(not, append)) -> c13(A(not, append), ENCARG(not)) ENCARG(cons_a(cons, append)) -> c13(A(cons, append), ENCARG(cons)) ENCARG(cons_a(false, append)) -> c13(A(false, append), ENCARG(false)) ENCARG(cons_a(le, append)) -> c13(A(le, append), ENCARG(le)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, nil)) -> c13(A(encArg(x0), nil), ENCARG(x0)) by ENCARG(cons_a(append, nil)) -> c13(A(append, nil), ENCARG(append)) ENCARG(cons_a(nil, nil)) -> c13(A(nil, nil), ENCARG(nil)) ENCARG(cons_a(cons, nil)) -> c13(A(cons, nil), ENCARG(cons)) ENCARG(cons_a(filter, nil)) -> c13(A(filter, nil), ENCARG(filter)) ENCARG(cons_a(if, nil)) -> c13(A(if, nil), ENCARG(if)) ENCARG(cons_a(le, nil)) -> c13(A(le, nil), ENCARG(le)) ENCARG(cons_a(0, nil)) -> c13(A(0, nil), ENCARG(0)) ENCARG(cons_a(true, nil)) -> c13(A(true, nil), ENCARG(true)) ENCARG(cons_a(s, nil)) -> c13(A(s, nil), ENCARG(s)) ENCARG(cons_a(false, nil)) -> c13(A(false, nil), ENCARG(false)) ENCARG(cons_a(not, nil)) -> c13(A(not, nil), ENCARG(not)) ENCARG(cons_a(not2, nil)) -> c13(A(not2, nil), ENCARG(not2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), nil)) -> c13(A(a(encArg(z0), encArg(z1)), nil), ENCARG(cons_a(z0, z1))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(append, nil)) -> c13(A(append, nil), ENCARG(append)) ENCARG(cons_a(nil, nil)) -> c13(A(nil, nil), ENCARG(nil)) ENCARG(cons_a(cons, nil)) -> c13(A(cons, nil), ENCARG(cons)) ENCARG(cons_a(filter, nil)) -> c13(A(filter, nil), ENCARG(filter)) ENCARG(cons_a(if, nil)) -> c13(A(if, nil), ENCARG(if)) ENCARG(cons_a(le, nil)) -> c13(A(le, nil), ENCARG(le)) ENCARG(cons_a(0, nil)) -> c13(A(0, nil), ENCARG(0)) ENCARG(cons_a(true, nil)) -> c13(A(true, nil), ENCARG(true)) ENCARG(cons_a(s, nil)) -> c13(A(s, nil), ENCARG(s)) ENCARG(cons_a(false, nil)) -> c13(A(false, nil), ENCARG(false)) ENCARG(cons_a(not, nil)) -> c13(A(not, nil), ENCARG(not)) ENCARG(cons_a(not2, nil)) -> c13(A(not2, nil), ENCARG(not2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_a(0, nil)) -> c13(A(0, nil), ENCARG(0)) ENCARG(cons_a(true, nil)) -> c13(A(true, nil), ENCARG(true)) ENCARG(cons_a(filter, nil)) -> c13(A(filter, nil), ENCARG(filter)) ENCARG(cons_a(nil, nil)) -> c13(A(nil, nil), ENCARG(nil)) ENCARG(cons_a(append, nil)) -> c13(A(append, nil), ENCARG(append)) ENCARG(cons_a(not, nil)) -> c13(A(not, nil), ENCARG(not)) ENCARG(cons_a(le, nil)) -> c13(A(le, nil), ENCARG(le)) ENCARG(cons_a(not2, nil)) -> c13(A(not2, nil), ENCARG(not2)) ENCARG(cons_a(s, nil)) -> c13(A(s, nil), ENCARG(s)) ENCARG(cons_a(false, nil)) -> c13(A(false, nil), ENCARG(false)) ENCARG(cons_a(if, nil)) -> c13(A(if, nil), ENCARG(if)) ENCARG(cons_a(cons, nil)) -> c13(A(cons, nil), ENCARG(cons)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, cons)) -> c13(A(encArg(x0), cons), ENCARG(x0)) by ENCARG(cons_a(append, cons)) -> c13(A(append, cons), ENCARG(append)) ENCARG(cons_a(nil, cons)) -> c13(A(nil, cons), ENCARG(nil)) ENCARG(cons_a(cons, cons)) -> c13(A(cons, cons), ENCARG(cons)) ENCARG(cons_a(filter, cons)) -> c13(A(filter, cons), ENCARG(filter)) ENCARG(cons_a(if, cons)) -> c13(A(if, cons), ENCARG(if)) ENCARG(cons_a(le, cons)) -> c13(A(le, cons), ENCARG(le)) ENCARG(cons_a(0, cons)) -> c13(A(0, cons), ENCARG(0)) ENCARG(cons_a(true, cons)) -> c13(A(true, cons), ENCARG(true)) ENCARG(cons_a(s, cons)) -> c13(A(s, cons), ENCARG(s)) ENCARG(cons_a(false, cons)) -> c13(A(false, cons), ENCARG(false)) ENCARG(cons_a(not, cons)) -> c13(A(not, cons), ENCARG(not)) ENCARG(cons_a(not2, cons)) -> c13(A(not2, cons), ENCARG(not2)) ENCARG(cons_a(qs, cons)) -> c13(A(qs, cons), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), cons)) -> c13(A(a(encArg(z0), encArg(z1)), cons), ENCARG(cons_a(z0, z1))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(append, cons)) -> c13(A(append, cons), ENCARG(append)) ENCARG(cons_a(nil, cons)) -> c13(A(nil, cons), ENCARG(nil)) ENCARG(cons_a(cons, cons)) -> c13(A(cons, cons), ENCARG(cons)) ENCARG(cons_a(filter, cons)) -> c13(A(filter, cons), ENCARG(filter)) ENCARG(cons_a(if, cons)) -> c13(A(if, cons), ENCARG(if)) ENCARG(cons_a(le, cons)) -> c13(A(le, cons), ENCARG(le)) ENCARG(cons_a(0, cons)) -> c13(A(0, cons), ENCARG(0)) ENCARG(cons_a(true, cons)) -> c13(A(true, cons), ENCARG(true)) ENCARG(cons_a(s, cons)) -> c13(A(s, cons), ENCARG(s)) ENCARG(cons_a(false, cons)) -> c13(A(false, cons), ENCARG(false)) ENCARG(cons_a(not, cons)) -> c13(A(not, cons), ENCARG(not)) ENCARG(cons_a(not2, cons)) -> c13(A(not2, cons), ENCARG(not2)) ENCARG(cons_a(qs, cons)) -> c13(A(qs, cons), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(qs, cons)) -> c13(A(qs, cons), ENCARG(qs)) ENCARG(cons_a(not2, cons)) -> c13(A(not2, cons), ENCARG(not2)) ENCARG(cons_a(cons, cons)) -> c13(A(cons, cons), ENCARG(cons)) ENCARG(cons_a(nil, cons)) -> c13(A(nil, cons), ENCARG(nil)) ENCARG(cons_a(true, cons)) -> c13(A(true, cons), ENCARG(true)) ENCARG(cons_a(filter, cons)) -> c13(A(filter, cons), ENCARG(filter)) ENCARG(cons_a(append, cons)) -> c13(A(append, cons), ENCARG(append)) ENCARG(cons_a(s, cons)) -> c13(A(s, cons), ENCARG(s)) ENCARG(cons_a(false, cons)) -> c13(A(false, cons), ENCARG(false)) ENCARG(cons_a(0, cons)) -> c13(A(0, cons), ENCARG(0)) ENCARG(cons_a(not, cons)) -> c13(A(not, cons), ENCARG(not)) ENCARG(cons_a(if, cons)) -> c13(A(if, cons), ENCARG(if)) ENCARG(cons_a(le, cons)) -> c13(A(le, cons), ENCARG(le)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, filter)) -> c13(A(encArg(x0), filter), ENCARG(x0)) by ENCARG(cons_a(append, filter)) -> c13(A(append, filter), ENCARG(append)) ENCARG(cons_a(nil, filter)) -> c13(A(nil, filter), ENCARG(nil)) ENCARG(cons_a(cons, filter)) -> c13(A(cons, filter), ENCARG(cons)) ENCARG(cons_a(filter, filter)) -> c13(A(filter, filter), ENCARG(filter)) ENCARG(cons_a(if, filter)) -> c13(A(if, filter), ENCARG(if)) ENCARG(cons_a(le, filter)) -> c13(A(le, filter), ENCARG(le)) ENCARG(cons_a(0, filter)) -> c13(A(0, filter), ENCARG(0)) ENCARG(cons_a(true, filter)) -> c13(A(true, filter), ENCARG(true)) ENCARG(cons_a(s, filter)) -> c13(A(s, filter), ENCARG(s)) ENCARG(cons_a(false, filter)) -> c13(A(false, filter), ENCARG(false)) ENCARG(cons_a(not, filter)) -> c13(A(not, filter), ENCARG(not)) ENCARG(cons_a(not2, filter)) -> c13(A(not2, filter), ENCARG(not2)) ENCARG(cons_a(qs, filter)) -> c13(A(qs, filter), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), filter)) -> c13(A(a(encArg(z0), encArg(z1)), filter), ENCARG(cons_a(z0, z1))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(append, filter)) -> c13(A(append, filter), ENCARG(append)) ENCARG(cons_a(nil, filter)) -> c13(A(nil, filter), ENCARG(nil)) ENCARG(cons_a(cons, filter)) -> c13(A(cons, filter), ENCARG(cons)) ENCARG(cons_a(filter, filter)) -> c13(A(filter, filter), ENCARG(filter)) ENCARG(cons_a(if, filter)) -> c13(A(if, filter), ENCARG(if)) ENCARG(cons_a(le, filter)) -> c13(A(le, filter), ENCARG(le)) ENCARG(cons_a(0, filter)) -> c13(A(0, filter), ENCARG(0)) ENCARG(cons_a(true, filter)) -> c13(A(true, filter), ENCARG(true)) ENCARG(cons_a(s, filter)) -> c13(A(s, filter), ENCARG(s)) ENCARG(cons_a(false, filter)) -> c13(A(false, filter), ENCARG(false)) ENCARG(cons_a(not, filter)) -> c13(A(not, filter), ENCARG(not)) ENCARG(cons_a(not2, filter)) -> c13(A(not2, filter), ENCARG(not2)) ENCARG(cons_a(qs, filter)) -> c13(A(qs, filter), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(if, filter)) -> c13(A(if, filter), ENCARG(if)) ENCARG(cons_a(append, filter)) -> c13(A(append, filter), ENCARG(append)) ENCARG(cons_a(0, filter)) -> c13(A(0, filter), ENCARG(0)) ENCARG(cons_a(le, filter)) -> c13(A(le, filter), ENCARG(le)) ENCARG(cons_a(not2, filter)) -> c13(A(not2, filter), ENCARG(not2)) ENCARG(cons_a(cons, filter)) -> c13(A(cons, filter), ENCARG(cons)) ENCARG(cons_a(not, filter)) -> c13(A(not, filter), ENCARG(not)) ENCARG(cons_a(nil, filter)) -> c13(A(nil, filter), ENCARG(nil)) ENCARG(cons_a(s, filter)) -> c13(A(s, filter), ENCARG(s)) ENCARG(cons_a(false, filter)) -> c13(A(false, filter), ENCARG(false)) ENCARG(cons_a(true, filter)) -> c13(A(true, filter), ENCARG(true)) ENCARG(cons_a(filter, filter)) -> c13(A(filter, filter), ENCARG(filter)) ENCARG(cons_a(qs, filter)) -> c13(A(qs, filter), ENCARG(qs)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, if)) -> c13(A(encArg(x0), if), ENCARG(x0)) by ENCARG(cons_a(append, if)) -> c13(A(append, if), ENCARG(append)) ENCARG(cons_a(nil, if)) -> c13(A(nil, if), ENCARG(nil)) ENCARG(cons_a(cons, if)) -> c13(A(cons, if), ENCARG(cons)) ENCARG(cons_a(filter, if)) -> c13(A(filter, if), ENCARG(filter)) ENCARG(cons_a(if, if)) -> c13(A(if, if), ENCARG(if)) ENCARG(cons_a(le, if)) -> c13(A(le, if), ENCARG(le)) ENCARG(cons_a(0, if)) -> c13(A(0, if), ENCARG(0)) ENCARG(cons_a(true, if)) -> c13(A(true, if), ENCARG(true)) ENCARG(cons_a(s, if)) -> c13(A(s, if), ENCARG(s)) ENCARG(cons_a(false, if)) -> c13(A(false, if), ENCARG(false)) ENCARG(cons_a(not, if)) -> c13(A(not, if), ENCARG(not)) ENCARG(cons_a(not2, if)) -> c13(A(not2, if), ENCARG(not2)) ENCARG(cons_a(qs, if)) -> c13(A(qs, if), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), if)) -> c13(A(a(encArg(z0), encArg(z1)), if), ENCARG(cons_a(z0, z1))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(append, if)) -> c13(A(append, if), ENCARG(append)) ENCARG(cons_a(nil, if)) -> c13(A(nil, if), ENCARG(nil)) ENCARG(cons_a(cons, if)) -> c13(A(cons, if), ENCARG(cons)) ENCARG(cons_a(filter, if)) -> c13(A(filter, if), ENCARG(filter)) ENCARG(cons_a(if, if)) -> c13(A(if, if), ENCARG(if)) ENCARG(cons_a(le, if)) -> c13(A(le, if), ENCARG(le)) ENCARG(cons_a(0, if)) -> c13(A(0, if), ENCARG(0)) ENCARG(cons_a(true, if)) -> c13(A(true, if), ENCARG(true)) ENCARG(cons_a(s, if)) -> c13(A(s, if), ENCARG(s)) ENCARG(cons_a(false, if)) -> c13(A(false, if), ENCARG(false)) ENCARG(cons_a(not, if)) -> c13(A(not, if), ENCARG(not)) ENCARG(cons_a(not2, if)) -> c13(A(not2, if), ENCARG(not2)) ENCARG(cons_a(qs, if)) -> c13(A(qs, if), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(false, if)) -> c13(A(false, if), ENCARG(false)) ENCARG(cons_a(s, if)) -> c13(A(s, if), ENCARG(s)) ENCARG(cons_a(0, if)) -> c13(A(0, if), ENCARG(0)) ENCARG(cons_a(append, if)) -> c13(A(append, if), ENCARG(append)) ENCARG(cons_a(nil, if)) -> c13(A(nil, if), ENCARG(nil)) ENCARG(cons_a(true, if)) -> c13(A(true, if), ENCARG(true)) ENCARG(cons_a(le, if)) -> c13(A(le, if), ENCARG(le)) ENCARG(cons_a(if, if)) -> c13(A(if, if), ENCARG(if)) ENCARG(cons_a(filter, if)) -> c13(A(filter, if), ENCARG(filter)) ENCARG(cons_a(not, if)) -> c13(A(not, if), ENCARG(not)) ENCARG(cons_a(cons, if)) -> c13(A(cons, if), ENCARG(cons)) ENCARG(cons_a(qs, if)) -> c13(A(qs, if), ENCARG(qs)) ENCARG(cons_a(not2, if)) -> c13(A(not2, if), ENCARG(not2)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, le)) -> c13(A(encArg(x0), le), ENCARG(x0)) by ENCARG(cons_a(append, le)) -> c13(A(append, le), ENCARG(append)) ENCARG(cons_a(nil, le)) -> c13(A(nil, le), ENCARG(nil)) ENCARG(cons_a(cons, le)) -> c13(A(cons, le), ENCARG(cons)) ENCARG(cons_a(filter, le)) -> c13(A(filter, le), ENCARG(filter)) ENCARG(cons_a(if, le)) -> c13(A(if, le), ENCARG(if)) ENCARG(cons_a(le, le)) -> c13(A(le, le), ENCARG(le)) ENCARG(cons_a(0, le)) -> c13(A(0, le), ENCARG(0)) ENCARG(cons_a(true, le)) -> c13(A(true, le), ENCARG(true)) ENCARG(cons_a(s, le)) -> c13(A(s, le), ENCARG(s)) ENCARG(cons_a(false, le)) -> c13(A(false, le), ENCARG(false)) ENCARG(cons_a(not, le)) -> c13(A(not, le), ENCARG(not)) ENCARG(cons_a(not2, le)) -> c13(A(not2, le), ENCARG(not2)) ENCARG(cons_a(qs, le)) -> c13(A(qs, le), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), le)) -> c13(A(a(encArg(z0), encArg(z1)), le), ENCARG(cons_a(z0, z1))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(append, le)) -> c13(A(append, le), ENCARG(append)) ENCARG(cons_a(nil, le)) -> c13(A(nil, le), ENCARG(nil)) ENCARG(cons_a(cons, le)) -> c13(A(cons, le), ENCARG(cons)) ENCARG(cons_a(filter, le)) -> c13(A(filter, le), ENCARG(filter)) ENCARG(cons_a(if, le)) -> c13(A(if, le), ENCARG(if)) ENCARG(cons_a(le, le)) -> c13(A(le, le), ENCARG(le)) ENCARG(cons_a(0, le)) -> c13(A(0, le), ENCARG(0)) ENCARG(cons_a(true, le)) -> c13(A(true, le), ENCARG(true)) ENCARG(cons_a(s, le)) -> c13(A(s, le), ENCARG(s)) ENCARG(cons_a(false, le)) -> c13(A(false, le), ENCARG(false)) ENCARG(cons_a(not, le)) -> c13(A(not, le), ENCARG(not)) ENCARG(cons_a(not2, le)) -> c13(A(not2, le), ENCARG(not2)) ENCARG(cons_a(qs, le)) -> c13(A(qs, le), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(if, le)) -> c13(A(if, le), ENCARG(if)) ENCARG(cons_a(not2, le)) -> c13(A(not2, le), ENCARG(not2)) ENCARG(cons_a(0, le)) -> c13(A(0, le), ENCARG(0)) ENCARG(cons_a(false, le)) -> c13(A(false, le), ENCARG(false)) ENCARG(cons_a(le, le)) -> c13(A(le, le), ENCARG(le)) ENCARG(cons_a(cons, le)) -> c13(A(cons, le), ENCARG(cons)) ENCARG(cons_a(qs, le)) -> c13(A(qs, le), ENCARG(qs)) ENCARG(cons_a(s, le)) -> c13(A(s, le), ENCARG(s)) ENCARG(cons_a(not, le)) -> c13(A(not, le), ENCARG(not)) ENCARG(cons_a(true, le)) -> c13(A(true, le), ENCARG(true)) ENCARG(cons_a(filter, le)) -> c13(A(filter, le), ENCARG(filter)) ENCARG(cons_a(append, le)) -> c13(A(append, le), ENCARG(append)) ENCARG(cons_a(nil, le)) -> c13(A(nil, le), ENCARG(nil)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, 0)) -> c13(A(encArg(x0), 0), ENCARG(x0)) by ENCARG(cons_a(append, 0)) -> c13(A(append, 0), ENCARG(append)) ENCARG(cons_a(nil, 0)) -> c13(A(nil, 0), ENCARG(nil)) ENCARG(cons_a(cons, 0)) -> c13(A(cons, 0), ENCARG(cons)) ENCARG(cons_a(filter, 0)) -> c13(A(filter, 0), ENCARG(filter)) ENCARG(cons_a(if, 0)) -> c13(A(if, 0), ENCARG(if)) ENCARG(cons_a(le, 0)) -> c13(A(le, 0), ENCARG(le)) ENCARG(cons_a(0, 0)) -> c13(A(0, 0), ENCARG(0)) ENCARG(cons_a(true, 0)) -> c13(A(true, 0), ENCARG(true)) ENCARG(cons_a(s, 0)) -> c13(A(s, 0), ENCARG(s)) ENCARG(cons_a(false, 0)) -> c13(A(false, 0), ENCARG(false)) ENCARG(cons_a(not, 0)) -> c13(A(not, 0), ENCARG(not)) ENCARG(cons_a(not2, 0)) -> c13(A(not2, 0), ENCARG(not2)) ENCARG(cons_a(qs, 0)) -> c13(A(qs, 0), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), 0)) -> c13(A(a(encArg(z0), encArg(z1)), 0), ENCARG(cons_a(z0, z1))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(append, 0)) -> c13(A(append, 0), ENCARG(append)) ENCARG(cons_a(nil, 0)) -> c13(A(nil, 0), ENCARG(nil)) ENCARG(cons_a(cons, 0)) -> c13(A(cons, 0), ENCARG(cons)) ENCARG(cons_a(filter, 0)) -> c13(A(filter, 0), ENCARG(filter)) ENCARG(cons_a(if, 0)) -> c13(A(if, 0), ENCARG(if)) ENCARG(cons_a(le, 0)) -> c13(A(le, 0), ENCARG(le)) ENCARG(cons_a(0, 0)) -> c13(A(0, 0), ENCARG(0)) ENCARG(cons_a(true, 0)) -> c13(A(true, 0), ENCARG(true)) ENCARG(cons_a(s, 0)) -> c13(A(s, 0), ENCARG(s)) ENCARG(cons_a(false, 0)) -> c13(A(false, 0), ENCARG(false)) ENCARG(cons_a(not, 0)) -> c13(A(not, 0), ENCARG(not)) ENCARG(cons_a(not2, 0)) -> c13(A(not2, 0), ENCARG(not2)) ENCARG(cons_a(qs, 0)) -> c13(A(qs, 0), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(true, 0)) -> c13(A(true, 0), ENCARG(true)) ENCARG(cons_a(filter, 0)) -> c13(A(filter, 0), ENCARG(filter)) ENCARG(cons_a(nil, 0)) -> c13(A(nil, 0), ENCARG(nil)) ENCARG(cons_a(append, 0)) -> c13(A(append, 0), ENCARG(append)) ENCARG(cons_a(le, 0)) -> c13(A(le, 0), ENCARG(le)) ENCARG(cons_a(s, 0)) -> c13(A(s, 0), ENCARG(s)) ENCARG(cons_a(0, 0)) -> c13(A(0, 0), ENCARG(0)) ENCARG(cons_a(if, 0)) -> c13(A(if, 0), ENCARG(if)) ENCARG(cons_a(cons, 0)) -> c13(A(cons, 0), ENCARG(cons)) ENCARG(cons_a(not, 0)) -> c13(A(not, 0), ENCARG(not)) ENCARG(cons_a(false, 0)) -> c13(A(false, 0), ENCARG(false)) ENCARG(cons_a(qs, 0)) -> c13(A(qs, 0), ENCARG(qs)) ENCARG(cons_a(not2, 0)) -> c13(A(not2, 0), ENCARG(not2)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, true)) -> c13(A(encArg(x0), true), ENCARG(x0)) by ENCARG(cons_a(append, true)) -> c13(A(append, true), ENCARG(append)) ENCARG(cons_a(nil, true)) -> c13(A(nil, true), ENCARG(nil)) ENCARG(cons_a(cons, true)) -> c13(A(cons, true), ENCARG(cons)) ENCARG(cons_a(filter, true)) -> c13(A(filter, true), ENCARG(filter)) ENCARG(cons_a(if, true)) -> c13(A(if, true), ENCARG(if)) ENCARG(cons_a(le, true)) -> c13(A(le, true), ENCARG(le)) ENCARG(cons_a(0, true)) -> c13(A(0, true), ENCARG(0)) ENCARG(cons_a(true, true)) -> c13(A(true, true), ENCARG(true)) ENCARG(cons_a(s, true)) -> c13(A(s, true), ENCARG(s)) ENCARG(cons_a(false, true)) -> c13(A(false, true), ENCARG(false)) ENCARG(cons_a(not, true)) -> c13(A(not, true), ENCARG(not)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true), ENCARG(not2)) ENCARG(cons_a(qs, true)) -> c13(A(qs, true), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), true)) -> c13(A(a(encArg(z0), encArg(z1)), true), ENCARG(cons_a(z0, z1))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(append, true)) -> c13(A(append, true), ENCARG(append)) ENCARG(cons_a(nil, true)) -> c13(A(nil, true), ENCARG(nil)) ENCARG(cons_a(cons, true)) -> c13(A(cons, true), ENCARG(cons)) ENCARG(cons_a(filter, true)) -> c13(A(filter, true), ENCARG(filter)) ENCARG(cons_a(if, true)) -> c13(A(if, true), ENCARG(if)) ENCARG(cons_a(le, true)) -> c13(A(le, true), ENCARG(le)) ENCARG(cons_a(0, true)) -> c13(A(0, true), ENCARG(0)) ENCARG(cons_a(true, true)) -> c13(A(true, true), ENCARG(true)) ENCARG(cons_a(s, true)) -> c13(A(s, true), ENCARG(s)) ENCARG(cons_a(false, true)) -> c13(A(false, true), ENCARG(false)) ENCARG(cons_a(not, true)) -> c13(A(not, true), ENCARG(not)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true), ENCARG(not2)) ENCARG(cons_a(qs, true)) -> c13(A(qs, true), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_a(nil, true)) -> c13(A(nil, true), ENCARG(nil)) ENCARG(cons_a(s, true)) -> c13(A(s, true), ENCARG(s)) ENCARG(cons_a(false, true)) -> c13(A(false, true), ENCARG(false)) ENCARG(cons_a(true, true)) -> c13(A(true, true), ENCARG(true)) ENCARG(cons_a(filter, true)) -> c13(A(filter, true), ENCARG(filter)) ENCARG(cons_a(0, true)) -> c13(A(0, true), ENCARG(0)) ENCARG(cons_a(append, true)) -> c13(A(append, true), ENCARG(append)) ENCARG(cons_a(if, true)) -> c13(A(if, true), ENCARG(if)) ENCARG(cons_a(not, true)) -> c13(A(not, true), ENCARG(not)) ENCARG(cons_a(le, true)) -> c13(A(le, true), ENCARG(le)) ENCARG(cons_a(qs, true)) -> c13(A(qs, true), ENCARG(qs)) ENCARG(cons_a(cons, true)) -> c13(A(cons, true), ENCARG(cons)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true), ENCARG(not2)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, s)) -> c13(A(encArg(x0), s), ENCARG(x0)) by ENCARG(cons_a(append, s)) -> c13(A(append, s), ENCARG(append)) ENCARG(cons_a(nil, s)) -> c13(A(nil, s), ENCARG(nil)) ENCARG(cons_a(cons, s)) -> c13(A(cons, s), ENCARG(cons)) ENCARG(cons_a(filter, s)) -> c13(A(filter, s), ENCARG(filter)) ENCARG(cons_a(if, s)) -> c13(A(if, s), ENCARG(if)) ENCARG(cons_a(le, s)) -> c13(A(le, s), ENCARG(le)) ENCARG(cons_a(0, s)) -> c13(A(0, s), ENCARG(0)) ENCARG(cons_a(true, s)) -> c13(A(true, s), ENCARG(true)) ENCARG(cons_a(s, s)) -> c13(A(s, s), ENCARG(s)) ENCARG(cons_a(false, s)) -> c13(A(false, s), ENCARG(false)) ENCARG(cons_a(not, s)) -> c13(A(not, s), ENCARG(not)) ENCARG(cons_a(not2, s)) -> c13(A(not2, s), ENCARG(not2)) ENCARG(cons_a(qs, s)) -> c13(A(qs, s), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), s)) -> c13(A(a(encArg(z0), encArg(z1)), s), ENCARG(cons_a(z0, z1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(append, s)) -> c13(A(append, s), ENCARG(append)) ENCARG(cons_a(nil, s)) -> c13(A(nil, s), ENCARG(nil)) ENCARG(cons_a(cons, s)) -> c13(A(cons, s), ENCARG(cons)) ENCARG(cons_a(filter, s)) -> c13(A(filter, s), ENCARG(filter)) ENCARG(cons_a(if, s)) -> c13(A(if, s), ENCARG(if)) ENCARG(cons_a(le, s)) -> c13(A(le, s), ENCARG(le)) ENCARG(cons_a(0, s)) -> c13(A(0, s), ENCARG(0)) ENCARG(cons_a(true, s)) -> c13(A(true, s), ENCARG(true)) ENCARG(cons_a(s, s)) -> c13(A(s, s), ENCARG(s)) ENCARG(cons_a(false, s)) -> c13(A(false, s), ENCARG(false)) ENCARG(cons_a(not, s)) -> c13(A(not, s), ENCARG(not)) ENCARG(cons_a(not2, s)) -> c13(A(not2, s), ENCARG(not2)) ENCARG(cons_a(qs, s)) -> c13(A(qs, s), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(if, s)) -> c13(A(if, s), ENCARG(if)) ENCARG(cons_a(not2, s)) -> c13(A(not2, s), ENCARG(not2)) ENCARG(cons_a(le, s)) -> c13(A(le, s), ENCARG(le)) ENCARG(cons_a(true, s)) -> c13(A(true, s), ENCARG(true)) ENCARG(cons_a(filter, s)) -> c13(A(filter, s), ENCARG(filter)) ENCARG(cons_a(nil, s)) -> c13(A(nil, s), ENCARG(nil)) ENCARG(cons_a(append, s)) -> c13(A(append, s), ENCARG(append)) ENCARG(cons_a(qs, s)) -> c13(A(qs, s), ENCARG(qs)) ENCARG(cons_a(0, s)) -> c13(A(0, s), ENCARG(0)) ENCARG(cons_a(false, s)) -> c13(A(false, s), ENCARG(false)) ENCARG(cons_a(s, s)) -> c13(A(s, s), ENCARG(s)) ENCARG(cons_a(cons, s)) -> c13(A(cons, s), ENCARG(cons)) ENCARG(cons_a(not, s)) -> c13(A(not, s), ENCARG(not)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, false)) -> c13(A(encArg(x0), false), ENCARG(x0)) by ENCARG(cons_a(append, false)) -> c13(A(append, false), ENCARG(append)) ENCARG(cons_a(nil, false)) -> c13(A(nil, false), ENCARG(nil)) ENCARG(cons_a(cons, false)) -> c13(A(cons, false), ENCARG(cons)) ENCARG(cons_a(filter, false)) -> c13(A(filter, false), ENCARG(filter)) ENCARG(cons_a(if, false)) -> c13(A(if, false), ENCARG(if)) ENCARG(cons_a(le, false)) -> c13(A(le, false), ENCARG(le)) ENCARG(cons_a(0, false)) -> c13(A(0, false), ENCARG(0)) ENCARG(cons_a(true, false)) -> c13(A(true, false), ENCARG(true)) ENCARG(cons_a(s, false)) -> c13(A(s, false), ENCARG(s)) ENCARG(cons_a(false, false)) -> c13(A(false, false), ENCARG(false)) ENCARG(cons_a(not, false)) -> c13(A(not, false), ENCARG(not)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false), ENCARG(not2)) ENCARG(cons_a(qs, false)) -> c13(A(qs, false), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), false)) -> c13(A(a(encArg(z0), encArg(z1)), false), ENCARG(cons_a(z0, z1))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(append, false)) -> c13(A(append, false), ENCARG(append)) ENCARG(cons_a(nil, false)) -> c13(A(nil, false), ENCARG(nil)) ENCARG(cons_a(cons, false)) -> c13(A(cons, false), ENCARG(cons)) ENCARG(cons_a(filter, false)) -> c13(A(filter, false), ENCARG(filter)) ENCARG(cons_a(if, false)) -> c13(A(if, false), ENCARG(if)) ENCARG(cons_a(le, false)) -> c13(A(le, false), ENCARG(le)) ENCARG(cons_a(0, false)) -> c13(A(0, false), ENCARG(0)) ENCARG(cons_a(true, false)) -> c13(A(true, false), ENCARG(true)) ENCARG(cons_a(s, false)) -> c13(A(s, false), ENCARG(s)) ENCARG(cons_a(false, false)) -> c13(A(false, false), ENCARG(false)) ENCARG(cons_a(not, false)) -> c13(A(not, false), ENCARG(not)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false), ENCARG(not2)) ENCARG(cons_a(qs, false)) -> c13(A(qs, false), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_a(cons, false)) -> c13(A(cons, false), ENCARG(cons)) ENCARG(cons_a(append, false)) -> c13(A(append, false), ENCARG(append)) ENCARG(cons_a(s, false)) -> c13(A(s, false), ENCARG(s)) ENCARG(cons_a(true, false)) -> c13(A(true, false), ENCARG(true)) ENCARG(cons_a(filter, false)) -> c13(A(filter, false), ENCARG(filter)) ENCARG(cons_a(qs, false)) -> c13(A(qs, false), ENCARG(qs)) ENCARG(cons_a(0, false)) -> c13(A(0, false), ENCARG(0)) ENCARG(cons_a(nil, false)) -> c13(A(nil, false), ENCARG(nil)) ENCARG(cons_a(false, false)) -> c13(A(false, false), ENCARG(false)) ENCARG(cons_a(le, false)) -> c13(A(le, false), ENCARG(le)) ENCARG(cons_a(not, false)) -> c13(A(not, false), ENCARG(not)) ENCARG(cons_a(if, false)) -> c13(A(if, false), ENCARG(if)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false), ENCARG(not2)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, not)) -> c13(A(encArg(x0), not), ENCARG(x0)) by ENCARG(cons_a(append, not)) -> c13(A(append, not), ENCARG(append)) ENCARG(cons_a(nil, not)) -> c13(A(nil, not), ENCARG(nil)) ENCARG(cons_a(cons, not)) -> c13(A(cons, not), ENCARG(cons)) ENCARG(cons_a(filter, not)) -> c13(A(filter, not), ENCARG(filter)) ENCARG(cons_a(if, not)) -> c13(A(if, not), ENCARG(if)) ENCARG(cons_a(le, not)) -> c13(A(le, not), ENCARG(le)) ENCARG(cons_a(0, not)) -> c13(A(0, not), ENCARG(0)) ENCARG(cons_a(true, not)) -> c13(A(true, not), ENCARG(true)) ENCARG(cons_a(s, not)) -> c13(A(s, not), ENCARG(s)) ENCARG(cons_a(false, not)) -> c13(A(false, not), ENCARG(false)) ENCARG(cons_a(not, not)) -> c13(A(not, not), ENCARG(not)) ENCARG(cons_a(not2, not)) -> c13(A(not2, not), ENCARG(not2)) ENCARG(cons_a(qs, not)) -> c13(A(qs, not), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), not)) -> c13(A(a(encArg(z0), encArg(z1)), not), ENCARG(cons_a(z0, z1))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) ENCARG(cons_a(append, not)) -> c13(A(append, not), ENCARG(append)) ENCARG(cons_a(nil, not)) -> c13(A(nil, not), ENCARG(nil)) ENCARG(cons_a(cons, not)) -> c13(A(cons, not), ENCARG(cons)) ENCARG(cons_a(filter, not)) -> c13(A(filter, not), ENCARG(filter)) ENCARG(cons_a(if, not)) -> c13(A(if, not), ENCARG(if)) ENCARG(cons_a(le, not)) -> c13(A(le, not), ENCARG(le)) ENCARG(cons_a(0, not)) -> c13(A(0, not), ENCARG(0)) ENCARG(cons_a(true, not)) -> c13(A(true, not), ENCARG(true)) ENCARG(cons_a(s, not)) -> c13(A(s, not), ENCARG(s)) ENCARG(cons_a(false, not)) -> c13(A(false, not), ENCARG(false)) ENCARG(cons_a(not, not)) -> c13(A(not, not), ENCARG(not)) ENCARG(cons_a(not2, not)) -> c13(A(not2, not), ENCARG(not2)) ENCARG(cons_a(qs, not)) -> c13(A(qs, not), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(cons, not)) -> c13(A(cons, not), ENCARG(cons)) ENCARG(cons_a(not, not)) -> c13(A(not, not), ENCARG(not)) ENCARG(cons_a(not2, not)) -> c13(A(not2, not), ENCARG(not2)) ENCARG(cons_a(s, not)) -> c13(A(s, not), ENCARG(s)) ENCARG(cons_a(append, not)) -> c13(A(append, not), ENCARG(append)) ENCARG(cons_a(le, not)) -> c13(A(le, not), ENCARG(le)) ENCARG(cons_a(nil, not)) -> c13(A(nil, not), ENCARG(nil)) ENCARG(cons_a(true, not)) -> c13(A(true, not), ENCARG(true)) ENCARG(cons_a(0, not)) -> c13(A(0, not), ENCARG(0)) ENCARG(cons_a(filter, not)) -> c13(A(filter, not), ENCARG(filter)) ENCARG(cons_a(if, not)) -> c13(A(if, not), ENCARG(if)) ENCARG(cons_a(qs, not)) -> c13(A(qs, not), ENCARG(qs)) ENCARG(cons_a(false, not)) -> c13(A(false, not), ENCARG(false)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, not2)) -> c13(A(encArg(x0), not2), ENCARG(x0)) by ENCARG(cons_a(append, not2)) -> c13(A(append, not2), ENCARG(append)) ENCARG(cons_a(nil, not2)) -> c13(A(nil, not2), ENCARG(nil)) ENCARG(cons_a(cons, not2)) -> c13(A(cons, not2), ENCARG(cons)) ENCARG(cons_a(filter, not2)) -> c13(A(filter, not2), ENCARG(filter)) ENCARG(cons_a(if, not2)) -> c13(A(if, not2), ENCARG(if)) ENCARG(cons_a(le, not2)) -> c13(A(le, not2), ENCARG(le)) ENCARG(cons_a(0, not2)) -> c13(A(0, not2), ENCARG(0)) ENCARG(cons_a(true, not2)) -> c13(A(true, not2), ENCARG(true)) ENCARG(cons_a(s, not2)) -> c13(A(s, not2), ENCARG(s)) ENCARG(cons_a(false, not2)) -> c13(A(false, not2), ENCARG(false)) ENCARG(cons_a(not, not2)) -> c13(A(not, not2), ENCARG(not)) ENCARG(cons_a(not2, not2)) -> c13(A(not2, not2), ENCARG(not2)) ENCARG(cons_a(qs, not2)) -> c13(A(qs, not2), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), not2)) -> c13(A(a(encArg(z0), encArg(z1)), not2), ENCARG(cons_a(z0, z1))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) ENCARG(cons_a(append, not2)) -> c13(A(append, not2), ENCARG(append)) ENCARG(cons_a(nil, not2)) -> c13(A(nil, not2), ENCARG(nil)) ENCARG(cons_a(cons, not2)) -> c13(A(cons, not2), ENCARG(cons)) ENCARG(cons_a(filter, not2)) -> c13(A(filter, not2), ENCARG(filter)) ENCARG(cons_a(if, not2)) -> c13(A(if, not2), ENCARG(if)) ENCARG(cons_a(le, not2)) -> c13(A(le, not2), ENCARG(le)) ENCARG(cons_a(0, not2)) -> c13(A(0, not2), ENCARG(0)) ENCARG(cons_a(true, not2)) -> c13(A(true, not2), ENCARG(true)) ENCARG(cons_a(s, not2)) -> c13(A(s, not2), ENCARG(s)) ENCARG(cons_a(false, not2)) -> c13(A(false, not2), ENCARG(false)) ENCARG(cons_a(not, not2)) -> c13(A(not, not2), ENCARG(not)) ENCARG(cons_a(not2, not2)) -> c13(A(not2, not2), ENCARG(not2)) ENCARG(cons_a(qs, not2)) -> c13(A(qs, not2), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(0, not2)) -> c13(A(0, not2), ENCARG(0)) ENCARG(cons_a(not2, not2)) -> c13(A(not2, not2), ENCARG(not2)) ENCARG(cons_a(cons, not2)) -> c13(A(cons, not2), ENCARG(cons)) ENCARG(cons_a(if, not2)) -> c13(A(if, not2), ENCARG(if)) ENCARG(cons_a(not, not2)) -> c13(A(not, not2), ENCARG(not)) ENCARG(cons_a(qs, not2)) -> c13(A(qs, not2), ENCARG(qs)) ENCARG(cons_a(true, not2)) -> c13(A(true, not2), ENCARG(true)) ENCARG(cons_a(filter, not2)) -> c13(A(filter, not2), ENCARG(filter)) ENCARG(cons_a(append, not2)) -> c13(A(append, not2), ENCARG(append)) ENCARG(cons_a(nil, not2)) -> c13(A(nil, not2), ENCARG(nil)) ENCARG(cons_a(false, not2)) -> c13(A(false, not2), ENCARG(false)) ENCARG(cons_a(le, not2)) -> c13(A(le, not2), ENCARG(le)) ENCARG(cons_a(s, not2)) -> c13(A(s, not2), ENCARG(s)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_2, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(x0, qs)) -> c13(A(encArg(x0), qs), ENCARG(x0)) by ENCARG(cons_a(append, qs)) -> c13(A(append, qs), ENCARG(append)) ENCARG(cons_a(nil, qs)) -> c13(A(nil, qs), ENCARG(nil)) ENCARG(cons_a(cons, qs)) -> c13(A(cons, qs), ENCARG(cons)) ENCARG(cons_a(filter, qs)) -> c13(A(filter, qs), ENCARG(filter)) ENCARG(cons_a(if, qs)) -> c13(A(if, qs), ENCARG(if)) ENCARG(cons_a(le, qs)) -> c13(A(le, qs), ENCARG(le)) ENCARG(cons_a(0, qs)) -> c13(A(0, qs), ENCARG(0)) ENCARG(cons_a(true, qs)) -> c13(A(true, qs), ENCARG(true)) ENCARG(cons_a(s, qs)) -> c13(A(s, qs), ENCARG(s)) ENCARG(cons_a(false, qs)) -> c13(A(false, qs), ENCARG(false)) ENCARG(cons_a(not, qs)) -> c13(A(not, qs), ENCARG(not)) ENCARG(cons_a(not2, qs)) -> c13(A(not2, qs), ENCARG(not2)) ENCARG(cons_a(qs, qs)) -> c13(A(qs, qs), ENCARG(qs)) ENCARG(cons_a(cons_a(z0, z1), qs)) -> c13(A(a(encArg(z0), encArg(z1)), qs), ENCARG(cons_a(z0, z1))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) ENCARG(cons_a(append, qs)) -> c13(A(append, qs), ENCARG(append)) ENCARG(cons_a(nil, qs)) -> c13(A(nil, qs), ENCARG(nil)) ENCARG(cons_a(cons, qs)) -> c13(A(cons, qs), ENCARG(cons)) ENCARG(cons_a(filter, qs)) -> c13(A(filter, qs), ENCARG(filter)) ENCARG(cons_a(if, qs)) -> c13(A(if, qs), ENCARG(if)) ENCARG(cons_a(le, qs)) -> c13(A(le, qs), ENCARG(le)) ENCARG(cons_a(0, qs)) -> c13(A(0, qs), ENCARG(0)) ENCARG(cons_a(true, qs)) -> c13(A(true, qs), ENCARG(true)) ENCARG(cons_a(s, qs)) -> c13(A(s, qs), ENCARG(s)) ENCARG(cons_a(false, qs)) -> c13(A(false, qs), ENCARG(false)) ENCARG(cons_a(not, qs)) -> c13(A(not, qs), ENCARG(not)) ENCARG(cons_a(not2, qs)) -> c13(A(not2, qs), ENCARG(not2)) ENCARG(cons_a(qs, qs)) -> c13(A(qs, qs), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_1, c13_2, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_a(not2, qs)) -> c13(A(not2, qs), ENCARG(not2)) ENCARG(cons_a(if, qs)) -> c13(A(if, qs), ENCARG(if)) ENCARG(cons_a(false, qs)) -> c13(A(false, qs), ENCARG(false)) ENCARG(cons_a(le, qs)) -> c13(A(le, qs), ENCARG(le)) ENCARG(cons_a(not, qs)) -> c13(A(not, qs), ENCARG(not)) ENCARG(cons_a(s, qs)) -> c13(A(s, qs), ENCARG(s)) ENCARG(cons_a(qs, qs)) -> c13(A(qs, qs), ENCARG(qs)) ENCARG(cons_a(cons, qs)) -> c13(A(cons, qs), ENCARG(cons)) ENCARG(cons_a(0, qs)) -> c13(A(0, qs), ENCARG(0)) ENCARG(cons_a(true, qs)) -> c13(A(true, qs), ENCARG(true)) ENCARG(cons_a(filter, qs)) -> c13(A(filter, qs), ENCARG(filter)) ENCARG(cons_a(append, qs)) -> c13(A(append, qs), ENCARG(append)) ENCARG(cons_a(nil, qs)) -> c13(A(nil, qs), ENCARG(nil)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_1, c13_2, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(not2, x1)) -> c13(A(not2, encArg(x1)), ENCARG(x1)) by ENCARG(cons_a(not2, append)) -> c13(A(not2, append), ENCARG(append)) ENCARG(cons_a(not2, nil)) -> c13(A(not2, nil), ENCARG(nil)) ENCARG(cons_a(not2, cons)) -> c13(A(not2, cons), ENCARG(cons)) ENCARG(cons_a(not2, filter)) -> c13(A(not2, filter), ENCARG(filter)) ENCARG(cons_a(not2, if)) -> c13(A(not2, if), ENCARG(if)) ENCARG(cons_a(not2, le)) -> c13(A(not2, le), ENCARG(le)) ENCARG(cons_a(not2, 0)) -> c13(A(not2, 0), ENCARG(0)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true), ENCARG(true)) ENCARG(cons_a(not2, s)) -> c13(A(not2, s), ENCARG(s)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false), ENCARG(false)) ENCARG(cons_a(not2, not)) -> c13(A(not2, not), ENCARG(not)) ENCARG(cons_a(not2, not2)) -> c13(A(not2, not2), ENCARG(not2)) ENCARG(cons_a(not2, qs)) -> c13(A(not2, qs), ENCARG(qs)) ENCARG(cons_a(not2, cons_a(z0, z1))) -> c13(A(not2, a(encArg(z0), encArg(z1))), ENCARG(cons_a(z0, z1))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) ENCARG(cons_a(not2, append)) -> c13(A(not2, append), ENCARG(append)) ENCARG(cons_a(not2, nil)) -> c13(A(not2, nil), ENCARG(nil)) ENCARG(cons_a(not2, cons)) -> c13(A(not2, cons), ENCARG(cons)) ENCARG(cons_a(not2, filter)) -> c13(A(not2, filter), ENCARG(filter)) ENCARG(cons_a(not2, if)) -> c13(A(not2, if), ENCARG(if)) ENCARG(cons_a(not2, le)) -> c13(A(not2, le), ENCARG(le)) ENCARG(cons_a(not2, 0)) -> c13(A(not2, 0), ENCARG(0)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true), ENCARG(true)) ENCARG(cons_a(not2, s)) -> c13(A(not2, s), ENCARG(s)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false), ENCARG(false)) ENCARG(cons_a(not2, not)) -> c13(A(not2, not), ENCARG(not)) ENCARG(cons_a(not2, not2)) -> c13(A(not2, not2), ENCARG(not2)) ENCARG(cons_a(not2, qs)) -> c13(A(not2, qs), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_1, c13_2, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 11 trailing nodes: ENCARG(cons_a(not2, append)) -> c13(A(not2, append), ENCARG(append)) ENCARG(cons_a(not2, qs)) -> c13(A(not2, qs), ENCARG(qs)) ENCARG(cons_a(not2, s)) -> c13(A(not2, s), ENCARG(s)) ENCARG(cons_a(not2, filter)) -> c13(A(not2, filter), ENCARG(filter)) ENCARG(cons_a(not2, le)) -> c13(A(not2, le), ENCARG(le)) ENCARG(cons_a(not2, cons)) -> c13(A(not2, cons), ENCARG(cons)) ENCARG(cons_a(not2, not2)) -> c13(A(not2, not2), ENCARG(not2)) ENCARG(cons_a(not2, if)) -> c13(A(not2, if), ENCARG(if)) ENCARG(cons_a(not2, not)) -> c13(A(not2, not), ENCARG(not)) ENCARG(cons_a(not2, 0)) -> c13(A(not2, 0), ENCARG(0)) ENCARG(cons_a(not2, nil)) -> c13(A(not2, nil), ENCARG(nil)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true), ENCARG(true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false), ENCARG(false)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_1, c13_2, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_1, c13_2, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(qs, x1)) -> c13(A(qs, encArg(x1)), ENCARG(x1)) by ENCARG(cons_a(qs, append)) -> c13(A(qs, append), ENCARG(append)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil), ENCARG(nil)) ENCARG(cons_a(qs, cons)) -> c13(A(qs, cons), ENCARG(cons)) ENCARG(cons_a(qs, filter)) -> c13(A(qs, filter), ENCARG(filter)) ENCARG(cons_a(qs, if)) -> c13(A(qs, if), ENCARG(if)) ENCARG(cons_a(qs, le)) -> c13(A(qs, le), ENCARG(le)) ENCARG(cons_a(qs, 0)) -> c13(A(qs, 0), ENCARG(0)) ENCARG(cons_a(qs, true)) -> c13(A(qs, true), ENCARG(true)) ENCARG(cons_a(qs, s)) -> c13(A(qs, s), ENCARG(s)) ENCARG(cons_a(qs, false)) -> c13(A(qs, false), ENCARG(false)) ENCARG(cons_a(qs, not)) -> c13(A(qs, not), ENCARG(not)) ENCARG(cons_a(qs, not2)) -> c13(A(qs, not2), ENCARG(not2)) ENCARG(cons_a(qs, qs)) -> c13(A(qs, qs), ENCARG(qs)) ENCARG(cons_a(qs, cons_a(z0, z1))) -> c13(A(qs, a(encArg(z0), encArg(z1))), ENCARG(cons_a(z0, z1))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) ENCARG(cons_a(qs, append)) -> c13(A(qs, append), ENCARG(append)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil), ENCARG(nil)) ENCARG(cons_a(qs, cons)) -> c13(A(qs, cons), ENCARG(cons)) ENCARG(cons_a(qs, filter)) -> c13(A(qs, filter), ENCARG(filter)) ENCARG(cons_a(qs, if)) -> c13(A(qs, if), ENCARG(if)) ENCARG(cons_a(qs, le)) -> c13(A(qs, le), ENCARG(le)) ENCARG(cons_a(qs, 0)) -> c13(A(qs, 0), ENCARG(0)) ENCARG(cons_a(qs, true)) -> c13(A(qs, true), ENCARG(true)) ENCARG(cons_a(qs, s)) -> c13(A(qs, s), ENCARG(s)) ENCARG(cons_a(qs, false)) -> c13(A(qs, false), ENCARG(false)) ENCARG(cons_a(qs, not)) -> c13(A(qs, not), ENCARG(not)) ENCARG(cons_a(qs, not2)) -> c13(A(qs, not2), ENCARG(not2)) ENCARG(cons_a(qs, qs)) -> c13(A(qs, qs), ENCARG(qs)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3, c13_2 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 12 trailing nodes: ENCARG(cons_a(qs, false)) -> c13(A(qs, false), ENCARG(false)) ENCARG(cons_a(qs, append)) -> c13(A(qs, append), ENCARG(append)) ENCARG(cons_a(qs, not2)) -> c13(A(qs, not2), ENCARG(not2)) ENCARG(cons_a(qs, not)) -> c13(A(qs, not), ENCARG(not)) ENCARG(cons_a(qs, s)) -> c13(A(qs, s), ENCARG(s)) ENCARG(cons_a(qs, true)) -> c13(A(qs, true), ENCARG(true)) ENCARG(cons_a(qs, filter)) -> c13(A(qs, filter), ENCARG(filter)) ENCARG(cons_a(qs, 0)) -> c13(A(qs, 0), ENCARG(0)) ENCARG(cons_a(qs, qs)) -> c13(A(qs, qs), ENCARG(qs)) ENCARG(cons_a(qs, cons)) -> c13(A(qs, cons), ENCARG(cons)) ENCARG(cons_a(qs, le)) -> c13(A(qs, le), ENCARG(le)) ENCARG(cons_a(qs, if)) -> c13(A(qs, if), ENCARG(if)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil), ENCARG(nil)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3, c13_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: encArg(append) -> append encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(if) -> if encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(not) -> not encArg(not2) -> not2 encArg(qs) -> qs encArg(cons_a(z0, z1)) -> a(encArg(z0), encArg(z1)) a(a(append, nil), z0) -> z0 a(a(append, a(a(cons, z0), z1)), z2) -> a(a(cons, z0), a(a(append, z1), z2)) a(a(filter, z0), nil) -> nil a(a(filter, z0), a(a(cons, z1), z2)) -> a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2)) a(a(le, 0), z0) -> true a(a(le, a(s, z0)), 0) -> false a(a(le, a(s, z0)), a(s, z1)) -> a(a(le, z0), z1) a(a(a(if, true), z0), z1) -> a(a(cons, z0), z1) a(a(a(if, false), z0), z1) -> z1 a(a(not, z0), z1) -> a(not2, a(z0, z1)) a(not2, true) -> false a(not2, false) -> true a(qs, nil) -> nil a(qs, a(a(cons, z0), z1)) -> a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1)))) Tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 ENCARG(cons_a(append, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(nil, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(cons, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(filter, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(if, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(le, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(0, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(true, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(s, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(false, x1)) -> c13(ENCARG(x1)) ENCARG(cons_a(not, x1)) -> c13(ENCARG(x1)) A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) ENCODE_A(x0, append) -> c(A(encArg(x0), append)) ENCODE_A(x0, nil) -> c(A(encArg(x0), nil)) ENCODE_A(x0, cons) -> c(A(encArg(x0), cons)) ENCODE_A(x0, filter) -> c(A(encArg(x0), filter)) ENCODE_A(x0, if) -> c(A(encArg(x0), if)) ENCODE_A(x0, le) -> c(A(encArg(x0), le)) ENCODE_A(x0, 0) -> c(A(encArg(x0), 0)) ENCODE_A(x0, true) -> c(A(encArg(x0), true)) ENCODE_A(x0, s) -> c(A(encArg(x0), s)) ENCODE_A(x0, false) -> c(A(encArg(x0), false)) ENCODE_A(x0, not) -> c(A(encArg(x0), not)) ENCODE_A(x0, not2) -> c(A(encArg(x0), not2)) ENCODE_A(x0, qs) -> c(A(encArg(x0), qs)) ENCODE_A(x0, cons_a(z0, z1)) -> c(A(encArg(x0), a(encArg(z0), encArg(z1)))) ENCODE_A(not2, x1) -> c(A(not2, encArg(x1))) ENCODE_A(qs, x1) -> c(A(qs, encArg(x1))) ENCODE_A(cons_a(z0, z1), x1) -> c(A(a(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_a(x0, cons_a(x1, append))) -> c13(A(encArg(x0), a(encArg(x1), append)), ENCARG(x0), ENCARG(cons_a(x1, append))) ENCARG(cons_a(x0, cons_a(x1, nil))) -> c13(A(encArg(x0), a(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_a(x1, nil))) ENCARG(cons_a(x0, cons_a(x1, cons))) -> c13(A(encArg(x0), a(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_a(x1, cons))) ENCARG(cons_a(x0, cons_a(x1, filter))) -> c13(A(encArg(x0), a(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_a(x1, filter))) ENCARG(cons_a(x0, cons_a(x1, if))) -> c13(A(encArg(x0), a(encArg(x1), if)), ENCARG(x0), ENCARG(cons_a(x1, if))) ENCARG(cons_a(x0, cons_a(x1, le))) -> c13(A(encArg(x0), a(encArg(x1), le)), ENCARG(x0), ENCARG(cons_a(x1, le))) ENCARG(cons_a(x0, cons_a(x1, 0))) -> c13(A(encArg(x0), a(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_a(x1, 0))) ENCARG(cons_a(x0, cons_a(x1, true))) -> c13(A(encArg(x0), a(encArg(x1), true)), ENCARG(x0), ENCARG(cons_a(x1, true))) ENCARG(cons_a(x0, cons_a(x1, s))) -> c13(A(encArg(x0), a(encArg(x1), s)), ENCARG(x0), ENCARG(cons_a(x1, s))) ENCARG(cons_a(x0, cons_a(x1, false))) -> c13(A(encArg(x0), a(encArg(x1), false)), ENCARG(x0), ENCARG(cons_a(x1, false))) ENCARG(cons_a(x0, cons_a(x1, not))) -> c13(A(encArg(x0), a(encArg(x1), not)), ENCARG(x0), ENCARG(cons_a(x1, not))) ENCARG(cons_a(x0, cons_a(x1, not2))) -> c13(A(encArg(x0), a(encArg(x1), not2)), ENCARG(x0), ENCARG(cons_a(x1, not2))) ENCARG(cons_a(x0, cons_a(x1, qs))) -> c13(A(encArg(x0), a(encArg(x1), qs)), ENCARG(x0), ENCARG(cons_a(x1, qs))) ENCARG(cons_a(x0, cons_a(x1, cons_a(z0, z1)))) -> c13(A(encArg(x0), a(encArg(x1), a(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_a(x1, cons_a(z0, z1)))) ENCARG(cons_a(x0, cons_a(append, x2))) -> c13(A(encArg(x0), a(append, encArg(x2))), ENCARG(x0), ENCARG(cons_a(append, x2))) ENCARG(cons_a(x0, cons_a(nil, x2))) -> c13(A(encArg(x0), a(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_a(nil, x2))) ENCARG(cons_a(x0, cons_a(cons, x2))) -> c13(A(encArg(x0), a(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons, x2))) ENCARG(cons_a(x0, cons_a(filter, x2))) -> c13(A(encArg(x0), a(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_a(filter, x2))) ENCARG(cons_a(x0, cons_a(if, x2))) -> c13(A(encArg(x0), a(if, encArg(x2))), ENCARG(x0), ENCARG(cons_a(if, x2))) ENCARG(cons_a(x0, cons_a(le, x2))) -> c13(A(encArg(x0), a(le, encArg(x2))), ENCARG(x0), ENCARG(cons_a(le, x2))) ENCARG(cons_a(x0, cons_a(0, x2))) -> c13(A(encArg(x0), a(0, encArg(x2))), ENCARG(x0), ENCARG(cons_a(0, x2))) ENCARG(cons_a(x0, cons_a(true, x2))) -> c13(A(encArg(x0), a(true, encArg(x2))), ENCARG(x0), ENCARG(cons_a(true, x2))) ENCARG(cons_a(x0, cons_a(s, x2))) -> c13(A(encArg(x0), a(s, encArg(x2))), ENCARG(x0), ENCARG(cons_a(s, x2))) ENCARG(cons_a(x0, cons_a(false, x2))) -> c13(A(encArg(x0), a(false, encArg(x2))), ENCARG(x0), ENCARG(cons_a(false, x2))) ENCARG(cons_a(x0, cons_a(not, x2))) -> c13(A(encArg(x0), a(not, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not, x2))) ENCARG(cons_a(x0, cons_a(not2, x2))) -> c13(A(encArg(x0), a(not2, encArg(x2))), ENCARG(x0), ENCARG(cons_a(not2, x2))) ENCARG(cons_a(x0, cons_a(qs, x2))) -> c13(A(encArg(x0), a(qs, encArg(x2))), ENCARG(x0), ENCARG(cons_a(qs, x2))) ENCARG(cons_a(x0, cons_a(cons_a(z0, z1), x2))) -> c13(A(encArg(x0), a(a(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_a(cons_a(z0, z1), x2))) ENCARG(cons_a(cons_a(z0, z1), cons_a(x1, x2))) -> c13(A(a(encArg(z0), encArg(z1)), a(encArg(x1), encArg(x2))), ENCARG(cons_a(z0, z1)), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(append, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(nil, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(filter, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(if, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(le, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(0, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(true, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(s, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(false, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not, cons_a(x1, x2))) -> c13(ENCARG(cons_a(x1, x2))) ENCARG(cons_a(not2, cons_a(x1, x2))) -> c13(A(not2, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(qs, cons_a(x1, x2))) -> c13(A(qs, a(encArg(x1), encArg(x2))), ENCARG(cons_a(x1, x2))) ENCARG(cons_a(cons_a(x0, append), x2)) -> c13(A(a(encArg(x0), append), encArg(x2)), ENCARG(cons_a(x0, append)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, nil), x2)) -> c13(A(a(encArg(x0), nil), encArg(x2)), ENCARG(cons_a(x0, nil)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons), x2)) -> c13(A(a(encArg(x0), cons), encArg(x2)), ENCARG(cons_a(x0, cons)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, filter), x2)) -> c13(A(a(encArg(x0), filter), encArg(x2)), ENCARG(cons_a(x0, filter)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, if), x2)) -> c13(A(a(encArg(x0), if), encArg(x2)), ENCARG(cons_a(x0, if)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, le), x2)) -> c13(A(a(encArg(x0), le), encArg(x2)), ENCARG(cons_a(x0, le)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, 0), x2)) -> c13(A(a(encArg(x0), 0), encArg(x2)), ENCARG(cons_a(x0, 0)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, true), x2)) -> c13(A(a(encArg(x0), true), encArg(x2)), ENCARG(cons_a(x0, true)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, s), x2)) -> c13(A(a(encArg(x0), s), encArg(x2)), ENCARG(cons_a(x0, s)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, false), x2)) -> c13(A(a(encArg(x0), false), encArg(x2)), ENCARG(cons_a(x0, false)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not), x2)) -> c13(A(a(encArg(x0), not), encArg(x2)), ENCARG(cons_a(x0, not)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, not2), x2)) -> c13(A(a(encArg(x0), not2), encArg(x2)), ENCARG(cons_a(x0, not2)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, qs), x2)) -> c13(A(a(encArg(x0), qs), encArg(x2)), ENCARG(cons_a(x0, qs)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, cons_a(z0, z1)), x2)) -> c13(A(a(encArg(x0), a(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_a(x0, cons_a(z0, z1))), ENCARG(x2)) ENCARG(cons_a(cons_a(append, x1), x2)) -> c13(A(a(append, encArg(x1)), encArg(x2)), ENCARG(cons_a(append, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(filter, x1), x2)) -> c13(A(a(filter, encArg(x1)), encArg(x2)), ENCARG(cons_a(filter, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(le, x1), x2)) -> c13(A(a(le, encArg(x1)), encArg(x2)), ENCARG(cons_a(le, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not, x1), x2)) -> c13(A(a(not, encArg(x1)), encArg(x2)), ENCARG(cons_a(not, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(not2, x1), x2)) -> c13(A(a(not2, encArg(x1)), encArg(x2)), ENCARG(cons_a(not2, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(qs, x1), x2)) -> c13(A(a(qs, encArg(x1)), encArg(x2)), ENCARG(cons_a(qs, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons_a(z0, z1), x1), x2)) -> c13(A(a(a(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_a(cons_a(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(x0, x1), append)) -> c13(A(a(encArg(x0), encArg(x1)), append), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), nil)) -> c13(A(a(encArg(x0), encArg(x1)), nil), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), cons)) -> c13(A(a(encArg(x0), encArg(x1)), cons), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), filter)) -> c13(A(a(encArg(x0), encArg(x1)), filter), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), if)) -> c13(A(a(encArg(x0), encArg(x1)), if), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), le)) -> c13(A(a(encArg(x0), encArg(x1)), le), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), 0)) -> c13(A(a(encArg(x0), encArg(x1)), 0), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), true)) -> c13(A(a(encArg(x0), encArg(x1)), true), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), s)) -> c13(A(a(encArg(x0), encArg(x1)), s), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), false)) -> c13(A(a(encArg(x0), encArg(x1)), false), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not)) -> c13(A(a(encArg(x0), encArg(x1)), not), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), not2)) -> c13(A(a(encArg(x0), encArg(x1)), not2), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(x0, x1), qs)) -> c13(A(a(encArg(x0), encArg(x1)), qs), ENCARG(cons_a(x0, x1))) ENCARG(cons_a(cons_a(nil, x1), x2)) -> c13(ENCARG(cons_a(nil, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(cons, x1), x2)) -> c13(ENCARG(cons_a(cons, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(if, x1), x2)) -> c13(ENCARG(cons_a(if, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(0, x1), x2)) -> c13(ENCARG(cons_a(0, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(true, x1), x2)) -> c13(ENCARG(cons_a(true, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(s, x1), x2)) -> c13(ENCARG(cons_a(s, x1)), ENCARG(x2)) ENCARG(cons_a(cons_a(false, x1), x2)) -> c13(ENCARG(cons_a(false, x1)), ENCARG(x2)) ENCARG(cons_a(qs, nil)) -> c13(A(qs, nil)) ENCARG(cons_a(not2, true)) -> c13(A(not2, true)) ENCARG(cons_a(not2, false)) -> c13(A(not2, false)) S tuples: A(a(append, nil), z0) -> c28 A(a(filter, z0), nil) -> c30 A(a(le, 0), z0) -> c32 A(a(le, a(s, z0)), 0) -> c33 A(a(a(if, false), z0), z1) -> c36 A(not2, true) -> c38 A(not2, false) -> c39 A(qs, nil) -> c40 A(a(append, a(a(cons, z0), z1)), z2) -> c29(A(a(append, z1), z2)) A(a(le, a(s, z0)), a(s, z1)) -> c34(A(a(le, z0), z1)) A(a(a(if, true), z0), z1) -> c35 A(a(not, a(filter, z0)), a(a(cons, z1), z2)) -> c37(A(not2, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(a(filter, z0), a(a(cons, z1), z2))) A(a(not, a(not, z0)), z1) -> c37(A(not2, a(not2, a(z0, z1))), A(a(not, z0), z1)) A(a(not, qs), a(a(cons, z0), z1)) -> c37(A(not2, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), A(qs, a(a(cons, z0), z1))) A(a(not, a(append, a(a(cons, z0), z1))), z2) -> c37(A(a(append, a(a(cons, z0), z1)), z2)) A(a(not, a(filter, z0)), nil) -> c37(A(a(filter, z0), nil)) A(a(not, a(a(if, true), z0)), z1) -> c37(A(a(a(if, true), z0), z1)) A(a(not, qs), nil) -> c37(A(qs, nil)) A(a(not, a(append, nil)), z0) -> c1(A(not2, z0)) A(a(not, a(append, nil)), z0) -> c1(A(a(append, nil), z0)) A(a(not, a(le, 0)), z0) -> c1(A(not2, true)) A(a(not, a(le, 0)), z0) -> c1(A(a(le, 0), z0)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(not2, false)) A(a(not, a(le, a(s, z0))), 0) -> c1(A(a(le, a(s, z0)), 0)) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(not2, a(a(le, z0), z1))) A(a(not, a(le, a(s, z0))), a(s, z1)) -> c1(A(a(le, a(s, z0)), a(s, z1))) A(a(not, a(a(if, false), z0)), z1) -> c1(A(not2, z1)) A(a(not, a(a(if, false), z0)), z1) -> c1(A(a(a(if, false), z0), z1)) A(a(not, not2), true) -> c1(A(not2, false)) A(a(not, not2), true) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, true)) A(a(not, not2), false) -> c1(A(not2, false)) A(a(filter, z0), a(a(cons, x1), nil)) -> c31(A(a(a(if, a(z0, x1)), x1), nil), A(z0, x1), A(a(filter, z0), nil)) A(a(filter, z0), a(a(cons, x1), a(a(cons, z1), z2))) -> c31(A(a(a(if, a(z0, x1)), x1), a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), A(z0, x1), A(a(filter, z0), a(a(cons, z1), z2))) A(a(filter, a(append, nil)), a(a(cons, z0), x2)) -> c31(A(a(a(if, z0), z0), a(a(filter, a(append, nil)), x2)), A(a(append, nil), z0), A(a(filter, a(append, nil)), x2)) A(a(filter, a(filter, z0)), a(a(cons, a(a(cons, z1), z2)), x2)) -> c31(A(a(a(if, a(a(a(if, a(z0, z1)), z1), a(a(filter, z0), z2))), a(a(cons, z1), z2)), a(a(filter, a(filter, z0)), x2)), A(a(filter, z0), a(a(cons, z1), z2)), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(le, 0)), a(a(cons, z0), x2)) -> c31(A(a(a(if, true), z0), a(a(filter, a(le, 0)), x2)), A(a(le, 0), z0), A(a(filter, a(le, 0)), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, 0), x2)) -> c31(A(a(a(if, false), 0), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), 0), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(le, a(s, z0))), a(a(cons, a(s, z1)), x2)) -> c31(A(a(a(if, a(a(le, z0), z1)), a(s, z1)), a(a(filter, a(le, a(s, z0))), x2)), A(a(le, a(s, z0)), a(s, z1)), A(a(filter, a(le, a(s, z0))), x2)) A(a(filter, a(a(if, false), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, z1), z1), a(a(filter, a(a(if, false), z0)), x2)), A(a(a(if, false), z0), z1), A(a(filter, a(a(if, false), z0)), x2)) A(a(filter, a(not, z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, a(not2, a(z0, z1))), z1), a(a(filter, a(not, z0)), x2)), A(a(not, z0), z1), A(a(filter, a(not, z0)), x2)) A(a(filter, not2), a(a(cons, true), x2)) -> c31(A(a(a(if, false), true), a(a(filter, not2), x2)), A(not2, true), A(a(filter, not2), x2)) A(a(filter, not2), a(a(cons, false), x2)) -> c31(A(a(a(if, true), false), a(a(filter, not2), x2)), A(not2, false), A(a(filter, not2), x2)) A(a(filter, qs), a(a(cons, a(a(cons, z0), z1)), x2)) -> c31(A(a(a(if, a(a(append, a(qs, a(a(filter, a(le, z0)), z1))), a(a(cons, z0), a(qs, a(a(filter, a(not, a(le, z0))), z1))))), a(a(cons, z0), z1)), a(a(filter, qs), x2)), A(qs, a(a(cons, z0), z1)), A(a(filter, qs), x2)) A(a(filter, a(append, a(a(cons, z0), z1))), a(a(cons, z2), x2)) -> c31(A(a(append, a(a(cons, z0), z1)), z2), A(a(filter, a(append, a(a(cons, z0), z1))), x2)) A(a(filter, a(filter, z0)), a(a(cons, nil), x2)) -> c31(A(a(filter, z0), nil), A(a(filter, a(filter, z0)), x2)) A(a(filter, a(a(if, true), z0)), a(a(cons, z1), x2)) -> c31(A(a(a(if, true), z0), z1), A(a(filter, a(a(if, true), z0)), x2)) A(a(filter, qs), a(a(cons, nil), x2)) -> c31(A(qs, nil), A(a(filter, qs), x2)) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), nil))), a(a(cons, x0), a(qs, nil))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2)))), a(a(cons, x0), a(qs, a(a(a(if, a(a(not, a(le, x0)), z1)), z1), a(a(filter, a(not, a(le, x0))), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), nil)) -> c41(A(a(append, a(qs, nil)), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), nil)))), A(qs, a(a(filter, a(le, x0)), nil)), A(a(filter, a(le, x0)), nil), A(qs, a(a(filter, a(not, a(le, x0))), nil)), A(a(filter, a(not, a(le, x0))), nil)) A(qs, a(a(cons, x0), a(a(cons, z1), z2))) -> c41(A(a(append, a(qs, a(a(a(if, a(a(le, x0), z1)), z1), a(a(filter, a(le, x0)), z2)))), a(a(cons, x0), a(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))))), A(qs, a(a(filter, a(le, x0)), a(a(cons, z1), z2))), A(a(filter, a(le, x0)), a(a(cons, z1), z2)), A(qs, a(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))), A(a(filter, a(not, a(le, x0))), a(a(cons, z1), z2))) A(qs, a(a(cons, x0), x1)) -> c41(A(a(filter, a(le, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, a_2 Defined Pair Symbols: A_2, ENCARG_1, ENCODE_A_2 Compound Symbols: c28, c30, c32, c33, c36, c38, c39, c40, c29_1, c34_1, c35, c13_1, c37_2, c37_1, c1_1, c31_3, c31_2, c41_5, c41_1, c_1, c13_3, c13_2