/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 220 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) 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), 124 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 23 ms] (26) CpxRNTS (27) SimplificationProof [BOTH BOUNDS(ID, ID), 16 ms] (28) CpxRNTS (29) CompletionProof [UPPER BOUND(ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 27 ms] (32) CpxRNTS (33) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (34) CdtProblem (35) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 15 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), 34 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 63 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 61 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 128 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 146 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 83 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms] (68) CdtProblem (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (78) CdtProblem (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 10 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(minus, 0), y) -> 0 app(app(minus, app(s, x)), 0) -> app(s, x) app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y) app(app(le, 0), y) -> true app(app(le, app(s, x)), 0) -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(perfectp, 0) -> false app(perfectp, app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) app(app(app(app(f, 0), y), 0), u) -> true app(app(app(app(f, 0), y), app(s, z)), u) -> false app(app(app(app(f, app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) app(app(app(app(f, app(s, x)), app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) app(app(map, fun), nil) -> nil app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) app(app(filter, fun), nil) -> nil app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), 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(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(minus, 0), y) -> 0 app(app(minus, app(s, x)), 0) -> app(s, x) app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y) app(app(le, 0), y) -> true app(app(le, app(s, x)), 0) -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(perfectp, 0) -> false app(perfectp, app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) app(app(app(app(f, 0), y), 0), u) -> true app(app(app(app(f, 0), y), app(s, z)), u) -> false app(app(app(app(f, app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) app(app(app(app(f, app(s, x)), app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) app(app(map, fun), nil) -> nil app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) app(app(filter, fun), nil) -> nil app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) The (relative) TRS S consists of the following rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(minus, 0), y) -> 0 app(app(minus, app(s, x)), 0) -> app(s, x) app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y) app(app(le, 0), y) -> true app(app(le, app(s, x)), 0) -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(perfectp, 0) -> false app(perfectp, app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) app(app(app(app(f, 0), y), 0), u) -> true app(app(app(app(f, 0), y), app(s, z)), u) -> false app(app(app(app(f, app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) app(app(app(app(f, app(s, x)), app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) app(app(map, fun), nil) -> nil app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) app(app(filter, fun), nil) -> nil app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) The (relative) TRS S consists of the following rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(minus, 0), y) -> 0 app(app(minus, app(s, x)), 0) -> app(s, x) app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y) app(app(le, 0), y) -> true app(app(le, app(s, x)), 0) -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(perfectp, 0) -> false app(perfectp, app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) app(app(app(app(f, 0), y), 0), u) -> true app(app(app(app(f, 0), y), app(s, z)), u) -> false app(app(app(app(f, app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) app(app(app(app(f, app(s, x)), app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) app(app(map, fun), nil) -> nil app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) app(app(filter, fun), nil) -> nil app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) The (relative) TRS S consists of the following rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 Rewrite Strategy: INNERMOST ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(minus, 0'), y) -> 0' app(app(minus, app(s, x)), 0') -> app(s, x) app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y) app(app(le, 0'), y) -> true app(app(le, app(s, x)), 0') -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(perfectp, 0') -> false app(perfectp, app(s, x)) -> app(app(app(app(f, x), app(s, 0')), app(s, x)), app(s, x)) app(app(app(app(f, 0'), y), 0'), u) -> true app(app(app(app(f, 0'), y), app(s, z)), u) -> false app(app(app(app(f, app(s, x)), 0'), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) app(app(app(app(f, app(s, x)), app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) app(app(map, fun), nil) -> nil app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) app(app(filter, fun), nil) -> nil app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) The (relative) TRS S consists of the following rules: encArg(minus) -> minus encArg(0') -> 0' encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_minus -> minus encode_0 -> 0' encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: app(app(minus, 0'), y) -> 0' app(app(minus, app(s, x)), 0') -> app(s, x) app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y) app(app(le, 0'), y) -> true app(app(le, app(s, x)), 0') -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(perfectp, 0') -> false app(perfectp, app(s, x)) -> app(app(app(app(f, x), app(s, 0')), app(s, x)), app(s, x)) app(app(app(app(f, 0'), y), 0'), u) -> true app(app(app(app(f, 0'), y), app(s, z)), u) -> false app(app(app(app(f, app(s, x)), 0'), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) app(app(app(app(f, app(s, x)), app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) app(app(map, fun), nil) -> nil app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) app(app(filter, fun), nil) -> nil app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) encArg(minus) -> minus encArg(0') -> 0' encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_minus -> minus encode_0 -> 0' encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 Types: app :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app minus :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app 0' :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app s :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app le :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app true :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app false :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app if :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app perfectp :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app f :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app map :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app nil :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app cons :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app filter :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app filter2 :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encArg :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app cons_app :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_app :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_minus :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_0 :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_s :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_le :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_true :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_false :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_if :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_perfectp :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_f :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_map :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_nil :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_cons :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_filter :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_filter2 :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app hole_minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app1_3 :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app gen_minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app2_3 :: Nat -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: app, encArg They will be analysed ascendingly in the following order: app < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: app(app(minus, 0'), y) -> 0' app(app(minus, app(s, x)), 0') -> app(s, x) app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y) app(app(le, 0'), y) -> true app(app(le, app(s, x)), 0') -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(perfectp, 0') -> false app(perfectp, app(s, x)) -> app(app(app(app(f, x), app(s, 0')), app(s, x)), app(s, x)) app(app(app(app(f, 0'), y), 0'), u) -> true app(app(app(app(f, 0'), y), app(s, z)), u) -> false app(app(app(app(f, app(s, x)), 0'), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) app(app(app(app(f, app(s, x)), app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) app(app(map, fun), nil) -> nil app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) app(app(filter, fun), nil) -> nil app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) encArg(minus) -> minus encArg(0') -> 0' encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_minus -> minus encode_0 -> 0' encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 Types: app :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app minus :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app 0' :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app s :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app le :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app true :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app false :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app if :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app perfectp :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app f :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app map :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app nil :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app cons :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app filter :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app filter2 :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encArg :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app cons_app :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_app :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_minus :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_0 :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_s :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_le :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_true :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_false :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_if :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_perfectp :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_f :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_map :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_nil :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_cons :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_filter :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app encode_filter2 :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app hole_minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app1_3 :: minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app gen_minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app2_3 :: Nat -> minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app Generator Equations: gen_minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app2_3(0) <=> minus gen_minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app2_3(+(x, 1)) <=> cons_app(minus, gen_minus:0':s:le:true:false:if:perfectp:f:map:nil:cons:filter:filter2:cons_app2_3(x)) The following defined symbols remain to be analysed: app, encArg They will be analysed ascendingly in the following order: app < encArg ---------------------------------------- (13) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (14) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(minus, 0), y) -> 0 app(app(minus, app(s, x)), 0) -> app(s, x) app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y) app(app(le, 0), y) -> true app(app(le, app(s, x)), 0) -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(perfectp, 0) -> false app(perfectp, app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) app(app(app(app(f, 0), y), 0), u) -> true app(app(app(app(f, 0), y), app(s, z)), u) -> false app(app(app(app(f, app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) app(app(app(app(f, app(s, x)), app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) app(app(map, fun), nil) -> nil app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) app(app(filter, fun), nil) -> nil app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (15) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(perfectp, 0) -> false app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) app(c_app(le, c_app(s, x)), 0) -> false app(c_app(c_app(c_app(f, 0), y), 0), u) -> true app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) app(c_app(c_app(if, false), x), y) -> y app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) app(c_app(map, fun), nil) -> nil app(c_app(filter, fun), nil) -> nil app(c_app(c_app(if, true), x), y) -> x app(c_app(minus, 0), y) -> 0 app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) app(c_app(minus, c_app(s, x)), 0) -> app(s, x) app(c_app(le, 0), y) -> true app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) app(perfectp, c_app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) app(c_app(c_app(c_app(f, 0), y), c_app(s, z)), u) -> false The (relative) TRS S consists of the following rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 app(x0, x1) -> c_app(x0, x1) Rewrite Strategy: INNERMOST ---------------------------------------- (17) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (18) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(perfectp, 0) -> false [1] app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(c_app(c_app(f, 0), y), 0), u) -> true [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) [1] app(c_app(map, fun), nil) -> nil [1] app(c_app(filter, fun), nil) -> nil [1] app(c_app(c_app(if, true), x), y) -> x [1] app(c_app(minus, 0), y) -> 0 [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) [1] app(c_app(minus, c_app(s, x)), 0) -> app(s, x) [1] app(c_app(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) [1] app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) [1] app(perfectp, c_app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) [1] app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) [1] app(c_app(c_app(c_app(f, 0), y), c_app(s, z)), u) -> false [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(if) -> if [0] encArg(perfectp) -> perfectp [0] encArg(f) -> f [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_if -> if [0] encode_perfectp -> perfectp [0] encode_f -> f [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] app(x0, x1) -> c_app(x0, x1) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (19) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (20) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(perfectp, 0) -> false [1] app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(c_app(c_app(f, 0), y), 0), u) -> true [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) [1] app(c_app(map, fun), nil) -> nil [1] app(c_app(filter, fun), nil) -> nil [1] app(c_app(c_app(if, true), x), y) -> x [1] app(c_app(minus, 0), y) -> 0 [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) [1] app(c_app(minus, c_app(s, x)), 0) -> app(s, x) [1] app(c_app(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) [1] app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) [1] app(perfectp, c_app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) [1] app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) [1] app(c_app(c_app(c_app(f, 0), y), c_app(s, z)), u) -> false [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(if) -> if [0] encArg(perfectp) -> perfectp [0] encArg(f) -> f [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_if -> if [0] encode_perfectp -> perfectp [0] encode_f -> f [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] app(x0, x1) -> c_app(x0, x1) [0] The TRS has the following type information: app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app 0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app c_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encArg :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app cons_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app encode_filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app Rewrite Strategy: INNERMOST ---------------------------------------- (21) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: encArg_1 encode_app_2 encode_minus encode_0 encode_s encode_le encode_true encode_false encode_if encode_perfectp encode_f encode_map encode_nil encode_cons encode_filter encode_filter2 app_2 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_if -> null_encode_if [0] encode_perfectp -> null_encode_perfectp [0] encode_f -> null_encode_f [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_minus, null_encode_0, null_encode_s, null_encode_le, null_encode_true, null_encode_false, null_encode_if, null_encode_perfectp, null_encode_f, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_app ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(perfectp, 0) -> false [1] app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(c_app(c_app(f, 0), y), 0), u) -> true [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) [1] app(c_app(map, fun), nil) -> nil [1] app(c_app(filter, fun), nil) -> nil [1] app(c_app(c_app(if, true), x), y) -> x [1] app(c_app(minus, 0), y) -> 0 [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) [1] app(c_app(minus, c_app(s, x)), 0) -> app(s, x) [1] app(c_app(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) [1] app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) [1] app(perfectp, c_app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) [1] app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) [1] app(c_app(c_app(c_app(f, 0), y), c_app(s, z)), u) -> false [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(if) -> if [0] encArg(perfectp) -> perfectp [0] encArg(f) -> f [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_if -> if [0] encode_perfectp -> perfectp [0] encode_f -> f [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_if -> null_encode_if [0] encode_perfectp -> null_encode_perfectp [0] encode_f -> null_encode_f [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app 0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app c_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encArg :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app cons_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encArg :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (23) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(perfectp, 0) -> false [1] app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(c_app(c_app(f, 0), y), 0), u) -> true [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(c_app(le, x), y)), app(app(app(app(f, c_app(s, x)), app(c_app(minus, y), x)), z), u)), app(app(app(c_app(f, x), u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(c_app(le, x), y)), app(app(app(app(f, c_app(s, x)), app(c_app(minus, y), x)), z), u)), app(app(app(null_app, u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(c_app(le, x), y)), app(app(app(app(f, c_app(s, x)), app(null_app, x)), z), u)), app(app(app(c_app(f, x), u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(c_app(le, x), y)), app(app(app(app(f, c_app(s, x)), app(null_app, x)), z), u)), app(app(app(null_app, u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(c_app(le, x), y)), app(app(app(app(f, null_app), app(c_app(minus, y), x)), z), u)), app(app(app(c_app(f, x), u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(c_app(le, x), y)), app(app(app(app(f, null_app), app(c_app(minus, y), x)), z), u)), app(app(app(null_app, u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(c_app(le, x), y)), app(app(app(app(f, null_app), app(null_app, x)), z), u)), app(app(app(c_app(f, x), u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(c_app(le, x), y)), app(app(app(app(f, null_app), app(null_app, x)), z), u)), app(app(app(null_app, u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(null_app, y)), app(app(app(app(f, c_app(s, x)), app(c_app(minus, y), x)), z), u)), app(app(app(c_app(f, x), u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(null_app, y)), app(app(app(app(f, c_app(s, x)), app(c_app(minus, y), x)), z), u)), app(app(app(null_app, u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(null_app, y)), app(app(app(app(f, c_app(s, x)), app(null_app, x)), z), u)), app(app(app(c_app(f, x), u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(null_app, y)), app(app(app(app(f, c_app(s, x)), app(null_app, x)), z), u)), app(app(app(null_app, u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(null_app, y)), app(app(app(app(f, null_app), app(c_app(minus, y), x)), z), u)), app(app(app(c_app(f, x), u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(null_app, y)), app(app(app(app(f, null_app), app(c_app(minus, y), x)), z), u)), app(app(app(null_app, u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(null_app, y)), app(app(app(app(f, null_app), app(null_app, x)), z), u)), app(app(app(c_app(f, x), u), z), u)) [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(null_app, y)), app(app(app(app(f, null_app), app(null_app, x)), z), u)), app(app(app(null_app, u), z), u)) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(c_app(filter, fun), xs) [1] app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(null_app, xs) [1] app(c_app(map, fun), nil) -> nil [1] app(c_app(filter, fun), nil) -> nil [1] app(c_app(c_app(if, true), x), y) -> x [1] app(c_app(minus, 0), y) -> 0 [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(c_app(le, x), y) [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(null_app, y) [1] app(c_app(minus, c_app(s, x)), 0) -> app(s, x) [1] app(c_app(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(c_app(cons, x), app(c_app(filter, fun), xs)) [1] app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(c_app(cons, x), app(null_app, xs)) [1] app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(null_app, app(c_app(filter, fun), xs)) [1] app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(null_app, app(null_app, xs)) [1] app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) [1] app(perfectp, c_app(s, x)) -> app(app(app(c_app(f, x), c_app(s, 0)), c_app(s, x)), c_app(s, x)) [1] app(perfectp, c_app(s, x)) -> app(app(app(c_app(f, x), c_app(s, 0)), c_app(s, x)), null_app) [1] app(perfectp, c_app(s, x)) -> app(app(app(c_app(f, x), c_app(s, 0)), null_app), c_app(s, x)) [1] app(perfectp, c_app(s, x)) -> app(app(app(c_app(f, x), c_app(s, 0)), null_app), null_app) [1] app(perfectp, c_app(s, x)) -> app(app(app(c_app(f, x), null_app), c_app(s, x)), c_app(s, x)) [1] app(perfectp, c_app(s, x)) -> app(app(app(c_app(f, x), null_app), c_app(s, x)), null_app) [1] app(perfectp, c_app(s, x)) -> app(app(app(c_app(f, x), null_app), null_app), c_app(s, x)) [1] app(perfectp, c_app(s, x)) -> app(app(app(c_app(f, x), null_app), null_app), null_app) [1] app(perfectp, c_app(s, x)) -> app(app(app(null_app, c_app(s, 0)), c_app(s, x)), c_app(s, x)) [1] app(perfectp, c_app(s, x)) -> app(app(app(null_app, c_app(s, 0)), c_app(s, x)), null_app) [1] app(perfectp, c_app(s, x)) -> app(app(app(null_app, c_app(s, 0)), null_app), c_app(s, x)) [1] app(perfectp, c_app(s, x)) -> app(app(app(null_app, c_app(s, 0)), null_app), null_app) [1] app(perfectp, c_app(s, x)) -> app(app(app(null_app, null_app), c_app(s, x)), c_app(s, x)) [1] app(perfectp, c_app(s, x)) -> app(app(app(null_app, null_app), c_app(s, x)), null_app) [1] app(perfectp, c_app(s, x)) -> app(app(app(null_app, null_app), null_app), c_app(s, x)) [1] app(perfectp, c_app(s, x)) -> app(app(app(null_app, null_app), null_app), null_app) [1] app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(c_app(minus, x), y) [1] app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(null_app, y) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(c_app(f, x), u), app(c_app(minus, z), c_app(s, x))), u) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(c_app(f, x), u), app(c_app(minus, z), null_app)), u) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(c_app(f, x), u), app(null_app, c_app(s, x))), u) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(c_app(f, x), u), app(null_app, null_app)), u) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(null_app, u), app(c_app(minus, z), c_app(s, x))), u) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(null_app, u), app(c_app(minus, z), null_app)), u) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(null_app, u), app(null_app, c_app(s, x))), u) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(null_app, u), app(null_app, null_app)), u) [1] app(c_app(c_app(c_app(f, 0), y), c_app(s, z)), u) -> false [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(if) -> if [0] encArg(perfectp) -> perfectp [0] encArg(f) -> f [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_if -> if [0] encode_perfectp -> perfectp [0] encode_f -> f [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_if -> null_encode_if [0] encode_perfectp -> null_encode_perfectp [0] encode_f -> null_encode_f [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app 0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app c_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encArg :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app cons_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encArg :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (25) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: perfectp => 11 0 => 0 false => 3 map => 8 cons => 1 le => 7 s => 12 f => 2 true => 13 if => 6 minus => 9 filter2 => 5 filter => 4 nil => 10 null_encArg => 0 null_encode_app => 0 null_encode_minus => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_le => 0 null_encode_true => 0 null_encode_false => 0 null_encode_if => 0 null_encode_perfectp => 0 null_encode_f => 0 null_encode_map => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_encode_filter2 => 0 null_app => 0 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: app(z', z'') -{ 1 }-> x :|: z' = 1 + (1 + 6 + 13) + x, z'' = y, x >= 0, y >= 0 app(z', z'') -{ 1 }-> y :|: z' = 1 + (1 + 6 + 3) + x, z'' = y, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(app(5, app(fun, x)), fun), x), xs) :|: fun >= 0, xs >= 0, z' = 1 + 4 + fun, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 0), app(0, x)), z), u)), app(app(app(0, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 0), app(0, x)), z), u)), app(app(app(1 + 2 + x, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 0), app(1 + 9 + y, x)), z), u)), app(app(app(0, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 0), app(1 + 9 + y, x)), z), u)), app(app(app(1 + 2 + x, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 1 + 12 + x), app(0, x)), z), u)), app(app(app(0, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 1 + 12 + x), app(0, x)), z), u)), app(app(app(1 + 2 + x, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 1 + 12 + x), app(1 + 9 + y, x)), z), u)), app(app(app(0, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 1 + 12 + x), app(1 + 9 + y, x)), z), u)), app(app(app(1 + 2 + x, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 0), app(0, x)), z), u)), app(app(app(0, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 0), app(0, x)), z), u)), app(app(app(1 + 2 + x, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 0), app(1 + 9 + y, x)), z), u)), app(app(app(0, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 0), app(1 + 9 + y, x)), z), u)), app(app(app(1 + 2 + x, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 1 + 12 + x), app(0, x)), z), u)), app(app(app(0, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 1 + 12 + x), app(0, x)), z), u)), app(app(app(1 + 2 + x, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 1 + 12 + x), app(1 + 9 + y, x)), z), u)), app(app(app(0, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 1 + 12 + x), app(1 + 9 + y, x)), z), u)), app(app(app(1 + 2 + x, u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(0, u), app(0, 0)), u) :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(0, u), app(0, 1 + 12 + x)), u) :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(0, u), app(1 + 9 + z, 0)), u) :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(0, u), app(1 + 9 + z, 1 + 12 + x)), u) :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 0), 0), 0) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 0), 0), 1 + 12 + x) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 0), 1 + 12 + x), 0) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 0), 1 + 12 + x), 1 + 12 + x) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 1 + 12 + 0), 0), 0) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 1 + 12 + 0), 0), 1 + 12 + x) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 1 + 12 + 0), 1 + 12 + x), 0) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 1 + 12 + 0), 1 + 12 + x), 1 + 12 + x) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, u), app(0, 0)), u) :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, u), app(0, 1 + 12 + x)), u) :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, u), app(1 + 9 + z, 0)), u) :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, u), app(1 + 9 + z, 1 + 12 + x)), u) :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, 0), 0), 0) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, 0), 0), 1 + 12 + x) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, 0), 1 + 12 + x), 0) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, 0), 1 + 12 + x), 1 + 12 + x) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, 1 + 12 + 0), 0), 0) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, 1 + 12 + 0), 0), 1 + 12 + x) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, 1 + 12 + 0), 1 + 12 + x), 0) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, 1 + 12 + 0), 1 + 12 + x), 1 + 12 + x) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(1, app(fun, x)), app(app(8, fun), xs)) :|: fun >= 0, xs >= 0, z' = 1 + 8 + fun, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(12, x) :|: z'' = 0, z' = 1 + 9 + (1 + 12 + x), x >= 0 app(z', z'') -{ 1 }-> app(0, xs) :|: fun >= 0, xs >= 0, z' = 1 + (1 + (1 + 5 + 3) + fun) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(0, y) :|: z' = 1 + 7 + (1 + 12 + x), x >= 0, y >= 0, z'' = 1 + 12 + y app(z', z'') -{ 1 }-> app(0, y) :|: z' = 1 + 9 + (1 + 12 + x), x >= 0, y >= 0, z'' = 1 + 12 + y app(z', z'') -{ 1 }-> app(0, app(0, xs)) :|: fun >= 0, xs >= 0, z' = 1 + (1 + (1 + 5 + 13) + fun) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(0, app(1 + 4 + fun, xs)) :|: fun >= 0, xs >= 0, z' = 1 + (1 + (1 + 5 + 13) + fun) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(1 + 9 + x, y) :|: z' = 1 + 9 + (1 + 12 + x), x >= 0, y >= 0, z'' = 1 + 12 + y app(z', z'') -{ 1 }-> app(1 + 7 + x, y) :|: z' = 1 + 7 + (1 + 12 + x), x >= 0, y >= 0, z'' = 1 + 12 + y app(z', z'') -{ 1 }-> app(1 + 4 + fun, xs) :|: fun >= 0, xs >= 0, z' = 1 + (1 + (1 + 5 + 3) + fun) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(1 + 1 + x, app(0, xs)) :|: fun >= 0, xs >= 0, z' = 1 + (1 + (1 + 5 + 13) + fun) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(1 + 1 + x, app(1 + 4 + fun, xs)) :|: fun >= 0, xs >= 0, z' = 1 + (1 + (1 + 5 + 13) + fun) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> 3 :|: z'' = 0, z' = 11 app(z', z'') -{ 1 }-> 3 :|: z'' = 0, z' = 1 + 7 + (1 + 12 + x), x >= 0 app(z', z'') -{ 1 }-> 3 :|: z >= 0, y >= 0, z'' = u, z' = 1 + (1 + (1 + 2 + 0) + y) + (1 + 12 + z), u >= 0 app(z', z'') -{ 1 }-> 13 :|: z' = 1 + (1 + (1 + 2 + 0) + y) + 0, y >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> 13 :|: z' = 1 + 7 + 0, z'' = y, y >= 0 app(z', z'') -{ 1 }-> 10 :|: fun >= 0, z' = 1 + 8 + fun, z'' = 10 app(z', z'') -{ 1 }-> 10 :|: fun >= 0, z' = 1 + 4 + fun, z'' = 10 app(z', z'') -{ 1 }-> 0 :|: z' = 1 + 9 + 0, z'' = y, y >= 0 app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 app(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0 encArg(z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2 encArg(z') -{ 0 }-> 9 :|: z' = 9 encArg(z') -{ 0 }-> 8 :|: z' = 8 encArg(z') -{ 0 }-> 7 :|: z' = 7 encArg(z') -{ 0 }-> 6 :|: z' = 6 encArg(z') -{ 0 }-> 5 :|: z' = 5 encArg(z') -{ 0 }-> 4 :|: z' = 4 encArg(z') -{ 0 }-> 3 :|: z' = 3 encArg(z') -{ 0 }-> 2 :|: z' = 2 encArg(z') -{ 0 }-> 13 :|: z' = 13 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_app(z', z'') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2 encode_app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 encode_cons -{ 0 }-> 1 :|: encode_cons -{ 0 }-> 0 :|: encode_f -{ 0 }-> 2 :|: encode_f -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 5 :|: encode_filter2 -{ 0 }-> 0 :|: encode_if -{ 0 }-> 6 :|: encode_if -{ 0 }-> 0 :|: encode_le -{ 0 }-> 7 :|: encode_le -{ 0 }-> 0 :|: encode_map -{ 0 }-> 8 :|: encode_map -{ 0 }-> 0 :|: encode_minus -{ 0 }-> 9 :|: encode_minus -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 10 :|: encode_nil -{ 0 }-> 0 :|: encode_perfectp -{ 0 }-> 11 :|: encode_perfectp -{ 0 }-> 0 :|: encode_s -{ 0 }-> 12 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 13 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (27) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: app(z', z'') -{ 1 }-> z'' :|: z' - 11 >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(app(5, app(z' - 5, x)), z' - 5), x), xs) :|: z' - 5 >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 0), app(0, x)), z), z'')), app(app(app(0, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 0), app(0, x)), z), z'')), app(app(app(1 + 2 + x, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 0), app(1 + 9 + y, x)), z), z'')), app(app(app(0, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 0), app(1 + 9 + y, x)), z), z'')), app(app(app(1 + 2 + x, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 1 + 12 + x), app(0, x)), z), z'')), app(app(app(0, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 1 + 12 + x), app(0, x)), z), z'')), app(app(app(1 + 2 + x, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 1 + 12 + x), app(1 + 9 + y, x)), z), z'')), app(app(app(0, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(0, y)), app(app(app(app(2, 1 + 12 + x), app(1 + 9 + y, x)), z), z'')), app(app(app(1 + 2 + x, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 0), app(0, x)), z), z'')), app(app(app(0, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 0), app(0, x)), z), z'')), app(app(app(1 + 2 + x, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 0), app(1 + 9 + y, x)), z), z'')), app(app(app(0, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 0), app(1 + 9 + y, x)), z), z'')), app(app(app(1 + 2 + x, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 1 + 12 + x), app(0, x)), z), z'')), app(app(app(0, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 1 + 12 + x), app(0, x)), z), z'')), app(app(app(1 + 2 + x, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 1 + 12 + x), app(1 + 9 + y, x)), z), z'')), app(app(app(0, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(1 + 7 + x, y)), app(app(app(app(2, 1 + 12 + x), app(1 + 9 + y, x)), z), z'')), app(app(app(1 + 2 + x, z''), z), z'')) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(0, z''), app(0, 0)), z'') :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(0, z''), app(0, 1 + 12 + x)), z'') :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(0, z''), app(1 + 9 + z, 0)), z'') :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(0, z''), app(1 + 9 + z, 1 + 12 + x)), z'') :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 0), 0), 0) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 0), 0), 1 + 12 + (z'' - 13)) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 0), 1 + 12 + (z'' - 13)), 0) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 0), 1 + 12 + (z'' - 13)), 1 + 12 + (z'' - 13)) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 1 + 12 + 0), 0), 0) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 1 + 12 + 0), 0), 1 + 12 + (z'' - 13)) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 1 + 12 + 0), 1 + 12 + (z'' - 13)), 0) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(0, 1 + 12 + 0), 1 + 12 + (z'' - 13)), 1 + 12 + (z'' - 13)) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, z''), app(0, 0)), z'') :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, z''), app(0, 1 + 12 + x)), z'') :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, z''), app(1 + 9 + z, 0)), z'') :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + x, z''), app(1 + 9 + z, 1 + 12 + x)), z'') :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + (z'' - 13), 0), 0), 0) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + (z'' - 13), 0), 0), 1 + 12 + (z'' - 13)) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + (z'' - 13), 0), 1 + 12 + (z'' - 13)), 0) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + (z'' - 13), 0), 1 + 12 + (z'' - 13)), 1 + 12 + (z'' - 13)) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + (z'' - 13), 1 + 12 + 0), 0), 0) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + (z'' - 13), 1 + 12 + 0), 0), 1 + 12 + (z'' - 13)) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + (z'' - 13), 1 + 12 + 0), 1 + 12 + (z'' - 13)), 0) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(1 + 2 + (z'' - 13), 1 + 12 + 0), 1 + 12 + (z'' - 13)), 1 + 12 + (z'' - 13)) :|: z' = 11, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(1, app(z' - 9, x)), app(app(8, z' - 9), xs)) :|: z' - 9 >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(12, z' - 23) :|: z'' = 0, z' - 23 >= 0 app(z', z'') -{ 1 }-> app(0, z'') :|: fun >= 0, z'' >= 0, z' = 1 + (1 + (1 + 5 + 3) + fun) + x, x >= 0 app(z', z'') -{ 1 }-> app(0, app(0, z'')) :|: fun >= 0, z'' >= 0, z' = 1 + (1 + (1 + 5 + 13) + fun) + x, x >= 0 app(z', z'') -{ 1 }-> app(0, app(1 + 4 + fun, z'')) :|: fun >= 0, z'' >= 0, z' = 1 + (1 + (1 + 5 + 13) + fun) + x, x >= 0 app(z', z'') -{ 1 }-> app(0, z'' - 13) :|: z' - 21 >= 0, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(0, z'' - 13) :|: z' - 23 >= 0, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(1 + 9 + (z' - 23), z'' - 13) :|: z' - 23 >= 0, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(1 + 7 + (z' - 21), z'' - 13) :|: z' - 21 >= 0, z'' - 13 >= 0 app(z', z'') -{ 1 }-> app(1 + 4 + fun, z'') :|: fun >= 0, z'' >= 0, z' = 1 + (1 + (1 + 5 + 3) + fun) + x, x >= 0 app(z', z'') -{ 1 }-> app(1 + 1 + x, app(0, z'')) :|: fun >= 0, z'' >= 0, z' = 1 + (1 + (1 + 5 + 13) + fun) + x, x >= 0 app(z', z'') -{ 1 }-> app(1 + 1 + x, app(1 + 4 + fun, z'')) :|: fun >= 0, z'' >= 0, z' = 1 + (1 + (1 + 5 + 13) + fun) + x, x >= 0 app(z', z'') -{ 1 }-> 3 :|: z'' = 0, z' = 11 app(z', z'') -{ 1 }-> 3 :|: z'' = 0, z' - 21 >= 0 app(z', z'') -{ 1 }-> 3 :|: z >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + 0) + y) + (1 + 12 + z), z'' >= 0 app(z', z'') -{ 1 }-> 13 :|: z' - 5 >= 0, z'' >= 0 app(z', z'') -{ 1 }-> 13 :|: z' = 1 + 7 + 0, z'' >= 0 app(z', z'') -{ 1 }-> 10 :|: z' - 9 >= 0, z'' = 10 app(z', z'') -{ 1 }-> 10 :|: z' - 5 >= 0, z'' = 10 app(z', z'') -{ 1 }-> 0 :|: z' = 1 + 9 + 0, z'' >= 0 app(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0 app(z', z'') -{ 1 }-> z' - 21 :|: z' - 21 >= 0, z'' >= 0 app(z', z'') -{ 0 }-> 1 + z' + z'' :|: z' >= 0, z'' >= 0 encArg(z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2 encArg(z') -{ 0 }-> 9 :|: z' = 9 encArg(z') -{ 0 }-> 8 :|: z' = 8 encArg(z') -{ 0 }-> 7 :|: z' = 7 encArg(z') -{ 0 }-> 6 :|: z' = 6 encArg(z') -{ 0 }-> 5 :|: z' = 5 encArg(z') -{ 0 }-> 4 :|: z' = 4 encArg(z') -{ 0 }-> 3 :|: z' = 3 encArg(z') -{ 0 }-> 2 :|: z' = 2 encArg(z') -{ 0 }-> 13 :|: z' = 13 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_app(z', z'') -{ 0 }-> app(encArg(z'), encArg(z'')) :|: z' >= 0, z'' >= 0 encode_app(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0 encode_cons -{ 0 }-> 1 :|: encode_cons -{ 0 }-> 0 :|: encode_f -{ 0 }-> 2 :|: encode_f -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 5 :|: encode_filter2 -{ 0 }-> 0 :|: encode_if -{ 0 }-> 6 :|: encode_if -{ 0 }-> 0 :|: encode_le -{ 0 }-> 7 :|: encode_le -{ 0 }-> 0 :|: encode_map -{ 0 }-> 8 :|: encode_map -{ 0 }-> 0 :|: encode_minus -{ 0 }-> 9 :|: encode_minus -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 10 :|: encode_nil -{ 0 }-> 0 :|: encode_perfectp -{ 0 }-> 11 :|: encode_perfectp -{ 0 }-> 0 :|: encode_s -{ 0 }-> 12 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 13 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (29) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_if -> null_encode_if [0] encode_perfectp -> null_encode_perfectp [0] encode_f -> null_encode_f [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_minus, null_encode_0, null_encode_s, null_encode_le, null_encode_true, null_encode_false, null_encode_if, null_encode_perfectp, null_encode_f, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_app ---------------------------------------- (30) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(perfectp, 0) -> false [1] app(c_app(map, fun), c_app(c_app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs)) [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(c_app(c_app(f, 0), y), 0), u) -> true [1] app(c_app(c_app(c_app(f, c_app(s, x)), c_app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u)) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs) [1] app(c_app(map, fun), nil) -> nil [1] app(c_app(filter, fun), nil) -> nil [1] app(c_app(c_app(if, true), x), y) -> x [1] app(c_app(minus, 0), y) -> 0 [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) [1] app(c_app(minus, c_app(s, x)), 0) -> app(s, x) [1] app(c_app(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs)) [1] app(c_app(filter, fun), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs) [1] app(perfectp, c_app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x)) [1] app(c_app(minus, c_app(s, x)), c_app(s, y)) -> app(app(minus, x), y) [1] app(c_app(c_app(c_app(f, c_app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u) [1] app(c_app(c_app(c_app(f, 0), y), c_app(s, z)), u) -> false [1] encArg(minus) -> minus [0] encArg(0) -> 0 [0] encArg(s) -> s [0] encArg(le) -> le [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(if) -> if [0] encArg(perfectp) -> perfectp [0] encArg(f) -> f [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_minus -> minus [0] encode_0 -> 0 [0] encode_s -> s [0] encode_le -> le [0] encode_true -> true [0] encode_false -> false [0] encode_if -> if [0] encode_perfectp -> perfectp [0] encode_f -> f [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_minus -> null_encode_minus [0] encode_0 -> null_encode_0 [0] encode_s -> null_encode_s [0] encode_le -> null_encode_le [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_if -> null_encode_if [0] encode_perfectp -> null_encode_perfectp [0] encode_f -> null_encode_f [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app 0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app c_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encArg :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app cons_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app -> perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app encode_filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encArg :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_minus :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_0 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_s :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_le :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_true :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_false :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_if :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_perfectp :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_f :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_map :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_nil :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_cons :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_filter :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_encode_filter2 :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app null_app :: perfectp:0:false:map:c_app:cons:le:s:f:true:if:minus:filter2:filter:nil:cons_app:null_encArg:null_encode_app:null_encode_minus:null_encode_0:null_encode_s:null_encode_le:null_encode_true:null_encode_false:null_encode_if:null_encode_perfectp:null_encode_f:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (31) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: perfectp => 11 0 => 0 false => 3 map => 8 cons => 1 le => 7 s => 12 f => 2 true => 13 if => 6 minus => 9 filter2 => 5 filter => 4 nil => 10 null_encArg => 0 null_encode_app => 0 null_encode_minus => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_le => 0 null_encode_true => 0 null_encode_false => 0 null_encode_if => 0 null_encode_perfectp => 0 null_encode_f => 0 null_encode_map => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_encode_filter2 => 0 null_app => 0 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: app(z', z'') -{ 1 }-> x :|: z' = 1 + (1 + 6 + 13) + x, z'' = y, x >= 0, y >= 0 app(z', z'') -{ 1 }-> y :|: z' = 1 + (1 + 6 + 3) + x, z'' = y, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(app(5, app(fun, x)), fun), x), xs) :|: fun >= 0, xs >= 0, z' = 1 + 4 + fun, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(app(app(app(2, x), u), app(app(9, z), app(12, x))), u) :|: z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + 0) + z, z >= 0, x >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(app(app(2, x), app(12, 0)), app(12, x)), app(12, x)) :|: z'' = 1 + 12 + x, z' = 11, x >= 0 app(z', z'') -{ 1 }-> app(app(app(6, app(app(7, x), y)), app(app(app(app(2, app(12, x)), app(app(9, y), x)), z), u)), app(app(app(app(2, x), u), z), u)) :|: z >= 0, x >= 0, y >= 0, z' = 1 + (1 + (1 + 2 + (1 + 12 + x)) + (1 + 12 + y)) + z, z'' = u, u >= 0 app(z', z'') -{ 1 }-> app(app(9, x), y) :|: z' = 1 + 9 + (1 + 12 + x), x >= 0, y >= 0, z'' = 1 + 12 + y app(z', z'') -{ 1 }-> app(app(7, x), y) :|: z' = 1 + 7 + (1 + 12 + x), x >= 0, y >= 0, z'' = 1 + 12 + y app(z', z'') -{ 1 }-> app(app(4, fun), xs) :|: fun >= 0, xs >= 0, z' = 1 + (1 + (1 + 5 + 3) + fun) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(app(1, x), app(app(4, fun), xs)) :|: fun >= 0, xs >= 0, z' = 1 + (1 + (1 + 5 + 13) + fun) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(app(1, app(fun, x)), app(app(8, fun), xs)) :|: fun >= 0, xs >= 0, z' = 1 + 8 + fun, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(12, x) :|: z'' = 0, z' = 1 + 9 + (1 + 12 + x), x >= 0 app(z', z'') -{ 1 }-> 3 :|: z'' = 0, z' = 11 app(z', z'') -{ 1 }-> 3 :|: z'' = 0, z' = 1 + 7 + (1 + 12 + x), x >= 0 app(z', z'') -{ 1 }-> 3 :|: z >= 0, y >= 0, z'' = u, z' = 1 + (1 + (1 + 2 + 0) + y) + (1 + 12 + z), u >= 0 app(z', z'') -{ 1 }-> 13 :|: z' = 1 + (1 + (1 + 2 + 0) + y) + 0, y >= 0, z'' = u, u >= 0 app(z', z'') -{ 1 }-> 13 :|: z' = 1 + 7 + 0, z'' = y, y >= 0 app(z', z'') -{ 1 }-> 10 :|: fun >= 0, z' = 1 + 8 + fun, z'' = 10 app(z', z'') -{ 1 }-> 10 :|: fun >= 0, z' = 1 + 4 + fun, z'' = 10 app(z', z'') -{ 1 }-> 0 :|: z' = 1 + 9 + 0, z'' = y, y >= 0 app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 app(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0 encArg(z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2 encArg(z') -{ 0 }-> 9 :|: z' = 9 encArg(z') -{ 0 }-> 8 :|: z' = 8 encArg(z') -{ 0 }-> 7 :|: z' = 7 encArg(z') -{ 0 }-> 6 :|: z' = 6 encArg(z') -{ 0 }-> 5 :|: z' = 5 encArg(z') -{ 0 }-> 4 :|: z' = 4 encArg(z') -{ 0 }-> 3 :|: z' = 3 encArg(z') -{ 0 }-> 2 :|: z' = 2 encArg(z') -{ 0 }-> 13 :|: z' = 13 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_app(z', z'') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2 encode_app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 encode_cons -{ 0 }-> 1 :|: encode_cons -{ 0 }-> 0 :|: encode_f -{ 0 }-> 2 :|: encode_f -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 5 :|: encode_filter2 -{ 0 }-> 0 :|: encode_if -{ 0 }-> 6 :|: encode_if -{ 0 }-> 0 :|: encode_le -{ 0 }-> 7 :|: encode_le -{ 0 }-> 0 :|: encode_map -{ 0 }-> 8 :|: encode_map -{ 0 }-> 0 :|: encode_minus -{ 0 }-> 9 :|: encode_minus -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 10 :|: encode_nil -{ 0 }-> 0 :|: encode_perfectp -{ 0 }-> 11 :|: encode_perfectp -{ 0 }-> 0 :|: encode_s -{ 0 }-> 12 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 13 :|: 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(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(minus) -> c ENCARG(0) -> c1 ENCARG(s) -> c2 ENCARG(le) -> c3 ENCARG(true) -> c4 ENCARG(false) -> c5 ENCARG(if) -> c6 ENCARG(perfectp) -> c7 ENCARG(f) -> c8 ENCARG(map) -> c9 ENCARG(nil) -> c10 ENCARG(cons) -> c11 ENCARG(filter) -> c12 ENCARG(filter2) -> c13 ENCARG(cons_app(z0, z1)) -> c14(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_MINUS -> c16 ENCODE_0 -> c17 ENCODE_S -> c18 ENCODE_LE -> c19 ENCODE_TRUE -> c20 ENCODE_FALSE -> c21 ENCODE_IF -> c22 ENCODE_PERFECTP -> c23 ENCODE_F -> c24 ENCODE_MAP -> c25 ENCODE_NIL -> c26 ENCODE_CONS -> c27 ENCODE_FILTER -> c28 ENCODE_FILTER2 -> c29 APP(app(minus, 0), z0) -> c30 APP(app(minus, app(s, z0)), 0) -> c31(APP(s, z0)) APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1), APP(minus, z0)) APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1), APP(le, z0)) APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)), APP(app(app(f, z0), app(s, 0)), app(s, z0)), APP(app(f, z0), app(s, 0)), APP(f, z0), APP(s, 0), APP(s, z0), APP(s, z0)) APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), APP(app(f, z0), z2), APP(f, z0), APP(app(minus, z1), app(s, z0)), APP(minus, z1), APP(s, z0)) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), APP(if, app(app(le, z0), z1)), APP(app(le, z0), z1), APP(le, z0), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), APP(app(f, app(s, z0)), app(app(minus, z1), z0)), APP(f, app(s, z0)), APP(s, z0), APP(app(minus, z1), z0), APP(minus, z1), APP(app(app(app(f, z0), z3), z2), z3), APP(app(app(f, z0), z3), z2), APP(app(f, z0), z3), APP(f, z0)) APP(app(map, z0), nil) -> c44 APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c46 APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(minus, app(s, z0)), 0) -> c31(APP(s, z0)) APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1), APP(minus, z0)) APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1), APP(le, z0)) APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)), APP(app(app(f, z0), app(s, 0)), app(s, z0)), APP(app(f, z0), app(s, 0)), APP(f, z0), APP(s, 0), APP(s, z0), APP(s, z0)) APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), APP(app(f, z0), z2), APP(f, z0), APP(app(minus, z1), app(s, z0)), APP(minus, z1), APP(s, z0)) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), APP(if, app(app(le, z0), z1)), APP(app(le, z0), z1), APP(le, z0), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), APP(app(f, app(s, z0)), app(app(minus, z1), z0)), APP(f, app(s, z0)), APP(s, z0), APP(app(minus, z1), z0), APP(minus, z1), APP(app(app(app(f, z0), z3), z2), z3), APP(app(app(f, z0), z3), z2), APP(app(f, z0), z3), APP(f, z0)) APP(app(map, z0), nil) -> c44 APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c46 APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_le, encode_true, encode_false, encode_if, encode_perfectp, encode_f, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, ENCODE_MINUS, ENCODE_0, ENCODE_S, ENCODE_LE, ENCODE_TRUE, ENCODE_FALSE, ENCODE_IF, ENCODE_PERFECTP, ENCODE_F, ENCODE_MAP, ENCODE_NIL, ENCODE_CONS, ENCODE_FILTER, ENCODE_FILTER2, APP_2 Compound Symbols: c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14_3, c15_3, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31_1, c32_2, c33, c34, c35_2, c36, c37, c38, c39_7, c40, c41, c42_7, c43_16, c44, c45_5, c46, c47_5, c48_4, c49_2 ---------------------------------------- (35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 28 trailing nodes: ENCODE_PERFECTP -> c23 ENCODE_0 -> c17 ENCARG(if) -> c6 ENCARG(filter2) -> c13 ENCODE_LE -> c19 ENCODE_IF -> c22 ENCODE_NIL -> c26 ENCARG(le) -> c3 ENCODE_TRUE -> c20 ENCARG(filter) -> c12 ENCARG(cons) -> c11 ENCARG(perfectp) -> c7 ENCODE_S -> c18 ENCODE_FALSE -> c21 ENCODE_MAP -> c25 ENCODE_F -> c24 ENCODE_FILTER -> c28 ENCODE_FILTER2 -> c29 ENCARG(f) -> c8 ENCARG(true) -> c4 ENCARG(s) -> c2 ENCARG(minus) -> c ENCARG(map) -> c9 ENCARG(0) -> c1 ENCODE_CONS -> c27 ENCODE_MINUS -> c16 ENCARG(nil) -> c10 ENCARG(false) -> c5 ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c14(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(minus, 0), z0) -> c30 APP(app(minus, app(s, z0)), 0) -> c31(APP(s, z0)) APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1), APP(minus, z0)) APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1), APP(le, z0)) APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)), APP(app(app(f, z0), app(s, 0)), app(s, z0)), APP(app(f, z0), app(s, 0)), APP(f, z0), APP(s, 0), APP(s, z0), APP(s, z0)) APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), APP(app(f, z0), z2), APP(f, z0), APP(app(minus, z1), app(s, z0)), APP(minus, z1), APP(s, z0)) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), APP(if, app(app(le, z0), z1)), APP(app(le, z0), z1), APP(le, z0), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), APP(app(f, app(s, z0)), app(app(minus, z1), z0)), APP(f, app(s, z0)), APP(s, z0), APP(app(minus, z1), z0), APP(minus, z1), APP(app(app(app(f, z0), z3), z2), z3), APP(app(app(f, z0), z3), z2), APP(app(f, z0), z3), APP(f, z0)) APP(app(map, z0), nil) -> c44 APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c46 APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(minus, app(s, z0)), 0) -> c31(APP(s, z0)) APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1), APP(minus, z0)) APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1), APP(le, z0)) APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)), APP(app(app(f, z0), app(s, 0)), app(s, z0)), APP(app(f, z0), app(s, 0)), APP(f, z0), APP(s, 0), APP(s, z0), APP(s, z0)) APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), APP(app(f, z0), z2), APP(f, z0), APP(app(minus, z1), app(s, z0)), APP(minus, z1), APP(s, z0)) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), APP(if, app(app(le, z0), z1)), APP(app(le, z0), z1), APP(le, z0), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), APP(app(f, app(s, z0)), app(app(minus, z1), z0)), APP(f, app(s, z0)), APP(s, z0), APP(app(minus, z1), z0), APP(minus, z1), APP(app(app(app(f, z0), z3), z2), z3), APP(app(app(f, z0), z3), z2), APP(app(f, z0), z3), APP(f, z0)) APP(app(map, z0), nil) -> c44 APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c46 APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_le, encode_true, encode_false, encode_if, encode_perfectp, encode_f, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c14_3, c15_3, c30, c31_1, c32_2, c33, c34, c35_2, c36, c37, c38, c39_7, c40, c41, c42_7, c43_16, c44, c45_5, c46, c47_5, c48_4, c49_2 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 35 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c14(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_le, encode_true, encode_false, encode_if, encode_perfectp, encode_f, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c14_3, c15_3, c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c43_5, c45_2, c47_2, c48_1, c49_1 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c14(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCODE_APP(z0, z1) -> c(ENCARG(z0)) ENCODE_APP(z0, z1) -> c(ENCARG(z1)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_le, encode_true, encode_false, encode_if, encode_perfectp, encode_f, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c14_3, c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c43_5, c45_2, c47_2, c48_1, c49_1, c_1 ---------------------------------------- (41) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_APP(z0, z1) -> c(ENCARG(z0)) ENCODE_APP(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c14(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_minus, encode_0, encode_s, encode_le, encode_true, encode_false, encode_if, encode_perfectp, encode_f, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c14_3, c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c43_5, c45_2, c47_2, c48_1, c49_1, c_1 ---------------------------------------- (43) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_minus -> minus encode_0 -> 0 encode_s -> s encode_le -> le encode_true -> true encode_false -> false encode_if -> if encode_perfectp -> perfectp encode_f -> f encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c14(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c14_3, c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c43_5, c45_2, c47_2, c48_1, c49_1, c_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c14(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0), ENCARG(minus)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0), ENCARG(le)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0), ENCARG(if)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0), ENCARG(perfectp)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0), ENCARG(f)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c14(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(minus, x1)) -> c14(APP(minus, encArg(x1)), ENCARG(minus), ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(APP(le, encArg(x1)), ENCARG(le), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(APP(if, encArg(x1)), ENCARG(if), ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(perfectp), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(APP(f, encArg(x1)), ENCARG(f), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0), ENCARG(minus)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0), ENCARG(le)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0), ENCARG(if)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0), ENCARG(perfectp)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0), ENCARG(f)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c14(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(minus, x1)) -> c14(APP(minus, encArg(x1)), ENCARG(minus), ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(APP(le, encArg(x1)), ENCARG(le), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(APP(if, encArg(x1)), ENCARG(if), ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(perfectp), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(APP(f, encArg(x1)), ENCARG(f), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c43_5, c45_2, c47_2, c48_1, c49_1, c_1, c14_3 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 41 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c14(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c43_5, c45_2, c47_2, c48_1, c49_1, c_1, c14_3, c14_2, c14_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)), APP(app(le, z0), z1), APP(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3), APP(app(minus, z1), z0), APP(app(app(app(f, z0), z3), z2), z3)) by APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c14(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c47_2, c48_1, c49_1, c_1, c14_3, c14_2, c14_1, c43_5 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c47(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) by APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, 0), app(minus, 0)), z0), x2), APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, app(s, z0)), app(minus, app(s, z0))), 0), x2), APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c14(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, 0), app(minus, 0)), z0), x2), APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, app(s, z0)), app(minus, app(s, z0))), 0), x2), APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, 0), app(minus, 0)), z0), x2), APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, app(s, z0)), app(minus, app(s, z0))), 0), x2), APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c_1, c14_3, c14_2, c14_1, c43_5, c47_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c14(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c_1, c14_3, c14_2, c14_1, c43_5, c47_2, c47_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(s, x1) -> c(APP(s, encArg(x1))) ENCODE_APP(le, x1) -> c(APP(le, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(if, x1) -> c(APP(if, encArg(x1))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(f, x1) -> c(APP(f, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c14(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(s, x1) -> c(APP(s, encArg(x1))) ENCODE_APP(le, x1) -> c(APP(le, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(if, x1) -> c(APP(if, encArg(x1))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(f, x1) -> c(APP(f, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_3, c14_2, c14_1, c43_5, c47_2, c47_1, c_1 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(minus, x1) -> c(APP(minus, encArg(x1))) ENCODE_APP(if, x1) -> c(APP(if, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(f, x1) -> c(APP(f, encArg(x1))) ENCODE_APP(s, x1) -> c(APP(s, encArg(x1))) ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(le, x1) -> c(APP(le, encArg(x1))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c14(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_3, c14_2, c14_1, c43_5, c47_2, c47_1, c_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c14(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(APP(minus, app(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(APP(le, app(encArg(x1), encArg(x2))), ENCARG(le), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(APP(if, app(encArg(x1), encArg(x2))), ENCARG(if), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(perfectp), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(APP(f, app(encArg(x1), encArg(x2))), ENCARG(f), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(APP(minus, app(encArg(x1), encArg(x2))), ENCARG(minus), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(APP(le, app(encArg(x1), encArg(x2))), ENCARG(le), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(APP(if, app(encArg(x1), encArg(x2))), ENCARG(if), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(perfectp), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(APP(f, app(encArg(x1), encArg(x2))), ENCARG(f), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_3, c14_2, c14_1, c43_5, c47_2, c47_1, c_1 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 27 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_3, c14_2, c14_1, c43_5, c47_2, c47_1, c_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c14(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)), ENCARG(minus)) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0)) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s)) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1)), ENCARG(le)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1)), ENCARG(if)) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1)), ENCARG(perfectp)) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)), ENCARG(f)) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2)) ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c14(APP(app(encArg(x0), encArg(x1)), app(encArg(z0), encArg(z1))), ENCARG(cons_app(x0, x1)), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(APP(app(if, encArg(x1)), encArg(x2)), ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(APP(app(f, encArg(x1)), encArg(x2)), ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1)), ENCARG(minus)) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0)) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s)) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1)), ENCARG(le)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1)), ENCARG(if)) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1)), ENCARG(perfectp)) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1)), ENCARG(f)) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2)) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(APP(app(if, encArg(x1)), encArg(x2)), ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(APP(app(f, encArg(x1)), encArg(x2)), ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 23 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, minus)) -> c14(APP(encArg(x0), minus), ENCARG(x0)) by ENCARG(cons_app(minus, minus)) -> c14(APP(minus, minus), ENCARG(minus)) ENCARG(cons_app(0, minus)) -> c14(APP(0, minus), ENCARG(0)) ENCARG(cons_app(s, minus)) -> c14(APP(s, minus), ENCARG(s)) ENCARG(cons_app(le, minus)) -> c14(APP(le, minus), ENCARG(le)) ENCARG(cons_app(true, minus)) -> c14(APP(true, minus), ENCARG(true)) ENCARG(cons_app(false, minus)) -> c14(APP(false, minus), ENCARG(false)) ENCARG(cons_app(if, minus)) -> c14(APP(if, minus), ENCARG(if)) ENCARG(cons_app(perfectp, minus)) -> c14(APP(perfectp, minus), ENCARG(perfectp)) ENCARG(cons_app(f, minus)) -> c14(APP(f, minus), ENCARG(f)) ENCARG(cons_app(map, minus)) -> c14(APP(map, minus), ENCARG(map)) ENCARG(cons_app(nil, minus)) -> c14(APP(nil, minus), ENCARG(nil)) ENCARG(cons_app(cons, minus)) -> c14(APP(cons, minus), ENCARG(cons)) ENCARG(cons_app(filter, minus)) -> c14(APP(filter, minus), ENCARG(filter)) ENCARG(cons_app(filter2, minus)) -> c14(APP(filter2, minus), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), minus)) -> c14(APP(app(encArg(z0), encArg(z1)), minus), ENCARG(cons_app(z0, z1))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(minus, minus)) -> c14(APP(minus, minus), ENCARG(minus)) ENCARG(cons_app(0, minus)) -> c14(APP(0, minus), ENCARG(0)) ENCARG(cons_app(s, minus)) -> c14(APP(s, minus), ENCARG(s)) ENCARG(cons_app(le, minus)) -> c14(APP(le, minus), ENCARG(le)) ENCARG(cons_app(true, minus)) -> c14(APP(true, minus), ENCARG(true)) ENCARG(cons_app(false, minus)) -> c14(APP(false, minus), ENCARG(false)) ENCARG(cons_app(if, minus)) -> c14(APP(if, minus), ENCARG(if)) ENCARG(cons_app(perfectp, minus)) -> c14(APP(perfectp, minus), ENCARG(perfectp)) ENCARG(cons_app(f, minus)) -> c14(APP(f, minus), ENCARG(f)) ENCARG(cons_app(map, minus)) -> c14(APP(map, minus), ENCARG(map)) ENCARG(cons_app(nil, minus)) -> c14(APP(nil, minus), ENCARG(nil)) ENCARG(cons_app(cons, minus)) -> c14(APP(cons, minus), ENCARG(cons)) ENCARG(cons_app(filter, minus)) -> c14(APP(filter, minus), ENCARG(filter)) ENCARG(cons_app(filter2, minus)) -> c14(APP(filter2, minus), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(true, minus)) -> c14(APP(true, minus), ENCARG(true)) ENCARG(cons_app(minus, minus)) -> c14(APP(minus, minus), ENCARG(minus)) ENCARG(cons_app(filter, minus)) -> c14(APP(filter, minus), ENCARG(filter)) ENCARG(cons_app(f, minus)) -> c14(APP(f, minus), ENCARG(f)) ENCARG(cons_app(s, minus)) -> c14(APP(s, minus), ENCARG(s)) ENCARG(cons_app(filter2, minus)) -> c14(APP(filter2, minus), ENCARG(filter2)) ENCARG(cons_app(map, minus)) -> c14(APP(map, minus), ENCARG(map)) ENCARG(cons_app(cons, minus)) -> c14(APP(cons, minus), ENCARG(cons)) ENCARG(cons_app(false, minus)) -> c14(APP(false, minus), ENCARG(false)) ENCARG(cons_app(if, minus)) -> c14(APP(if, minus), ENCARG(if)) ENCARG(cons_app(0, minus)) -> c14(APP(0, minus), ENCARG(0)) ENCARG(cons_app(perfectp, minus)) -> c14(APP(perfectp, minus), ENCARG(perfectp)) ENCARG(cons_app(le, minus)) -> c14(APP(le, minus), ENCARG(le)) ENCARG(cons_app(nil, minus)) -> c14(APP(nil, minus), ENCARG(nil)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, 0)) -> c14(APP(encArg(x0), 0), ENCARG(x0)) by ENCARG(cons_app(minus, 0)) -> c14(APP(minus, 0), ENCARG(minus)) ENCARG(cons_app(0, 0)) -> c14(APP(0, 0), ENCARG(0)) ENCARG(cons_app(s, 0)) -> c14(APP(s, 0), ENCARG(s)) ENCARG(cons_app(le, 0)) -> c14(APP(le, 0), ENCARG(le)) ENCARG(cons_app(true, 0)) -> c14(APP(true, 0), ENCARG(true)) ENCARG(cons_app(false, 0)) -> c14(APP(false, 0), ENCARG(false)) ENCARG(cons_app(if, 0)) -> c14(APP(if, 0), ENCARG(if)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0), ENCARG(perfectp)) ENCARG(cons_app(f, 0)) -> c14(APP(f, 0), ENCARG(f)) ENCARG(cons_app(map, 0)) -> c14(APP(map, 0), ENCARG(map)) ENCARG(cons_app(nil, 0)) -> c14(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(cons, 0)) -> c14(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(filter, 0)) -> c14(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(filter2, 0)) -> c14(APP(filter2, 0), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), 0)) -> c14(APP(app(encArg(z0), encArg(z1)), 0), ENCARG(cons_app(z0, z1))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(minus, 0)) -> c14(APP(minus, 0), ENCARG(minus)) ENCARG(cons_app(0, 0)) -> c14(APP(0, 0), ENCARG(0)) ENCARG(cons_app(s, 0)) -> c14(APP(s, 0), ENCARG(s)) ENCARG(cons_app(le, 0)) -> c14(APP(le, 0), ENCARG(le)) ENCARG(cons_app(true, 0)) -> c14(APP(true, 0), ENCARG(true)) ENCARG(cons_app(false, 0)) -> c14(APP(false, 0), ENCARG(false)) ENCARG(cons_app(if, 0)) -> c14(APP(if, 0), ENCARG(if)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0), ENCARG(perfectp)) ENCARG(cons_app(f, 0)) -> c14(APP(f, 0), ENCARG(f)) ENCARG(cons_app(map, 0)) -> c14(APP(map, 0), ENCARG(map)) ENCARG(cons_app(nil, 0)) -> c14(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(cons, 0)) -> c14(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(filter, 0)) -> c14(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(filter2, 0)) -> c14(APP(filter2, 0), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCARG(cons_app(0, 0)) -> c14(APP(0, 0), ENCARG(0)) ENCARG(cons_app(le, 0)) -> c14(APP(le, 0), ENCARG(le)) ENCARG(cons_app(map, 0)) -> c14(APP(map, 0), ENCARG(map)) ENCARG(cons_app(if, 0)) -> c14(APP(if, 0), ENCARG(if)) ENCARG(cons_app(filter, 0)) -> c14(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(filter2, 0)) -> c14(APP(filter2, 0), ENCARG(filter2)) ENCARG(cons_app(cons, 0)) -> c14(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(minus, 0)) -> c14(APP(minus, 0), ENCARG(minus)) ENCARG(cons_app(true, 0)) -> c14(APP(true, 0), ENCARG(true)) ENCARG(cons_app(nil, 0)) -> c14(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(false, 0)) -> c14(APP(false, 0), ENCARG(false)) ENCARG(cons_app(s, 0)) -> c14(APP(s, 0), ENCARG(s)) ENCARG(cons_app(f, 0)) -> c14(APP(f, 0), ENCARG(f)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0), ENCARG(perfectp)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, s)) -> c14(APP(encArg(x0), s), ENCARG(x0)) by ENCARG(cons_app(minus, s)) -> c14(APP(minus, s), ENCARG(minus)) ENCARG(cons_app(0, s)) -> c14(APP(0, s), ENCARG(0)) ENCARG(cons_app(s, s)) -> c14(APP(s, s), ENCARG(s)) ENCARG(cons_app(le, s)) -> c14(APP(le, s), ENCARG(le)) ENCARG(cons_app(true, s)) -> c14(APP(true, s), ENCARG(true)) ENCARG(cons_app(false, s)) -> c14(APP(false, s), ENCARG(false)) ENCARG(cons_app(if, s)) -> c14(APP(if, s), ENCARG(if)) ENCARG(cons_app(perfectp, s)) -> c14(APP(perfectp, s), ENCARG(perfectp)) ENCARG(cons_app(f, s)) -> c14(APP(f, s), ENCARG(f)) ENCARG(cons_app(map, s)) -> c14(APP(map, s), ENCARG(map)) ENCARG(cons_app(nil, s)) -> c14(APP(nil, s), ENCARG(nil)) ENCARG(cons_app(cons, s)) -> c14(APP(cons, s), ENCARG(cons)) ENCARG(cons_app(filter, s)) -> c14(APP(filter, s), ENCARG(filter)) ENCARG(cons_app(filter2, s)) -> c14(APP(filter2, s), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), s)) -> c14(APP(app(encArg(z0), encArg(z1)), s), ENCARG(cons_app(z0, z1))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, s)) -> c14(APP(minus, s), ENCARG(minus)) ENCARG(cons_app(0, s)) -> c14(APP(0, s), ENCARG(0)) ENCARG(cons_app(s, s)) -> c14(APP(s, s), ENCARG(s)) ENCARG(cons_app(le, s)) -> c14(APP(le, s), ENCARG(le)) ENCARG(cons_app(true, s)) -> c14(APP(true, s), ENCARG(true)) ENCARG(cons_app(false, s)) -> c14(APP(false, s), ENCARG(false)) ENCARG(cons_app(if, s)) -> c14(APP(if, s), ENCARG(if)) ENCARG(cons_app(perfectp, s)) -> c14(APP(perfectp, s), ENCARG(perfectp)) ENCARG(cons_app(f, s)) -> c14(APP(f, s), ENCARG(f)) ENCARG(cons_app(map, s)) -> c14(APP(map, s), ENCARG(map)) ENCARG(cons_app(nil, s)) -> c14(APP(nil, s), ENCARG(nil)) ENCARG(cons_app(cons, s)) -> c14(APP(cons, s), ENCARG(cons)) ENCARG(cons_app(filter, s)) -> c14(APP(filter, s), ENCARG(filter)) ENCARG(cons_app(filter2, s)) -> c14(APP(filter2, s), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(if, s)) -> c14(APP(if, s), ENCARG(if)) ENCARG(cons_app(nil, s)) -> c14(APP(nil, s), ENCARG(nil)) ENCARG(cons_app(true, s)) -> c14(APP(true, s), ENCARG(true)) ENCARG(cons_app(minus, s)) -> c14(APP(minus, s), ENCARG(minus)) ENCARG(cons_app(perfectp, s)) -> c14(APP(perfectp, s), ENCARG(perfectp)) ENCARG(cons_app(le, s)) -> c14(APP(le, s), ENCARG(le)) ENCARG(cons_app(0, s)) -> c14(APP(0, s), ENCARG(0)) ENCARG(cons_app(filter, s)) -> c14(APP(filter, s), ENCARG(filter)) ENCARG(cons_app(filter2, s)) -> c14(APP(filter2, s), ENCARG(filter2)) ENCARG(cons_app(false, s)) -> c14(APP(false, s), ENCARG(false)) ENCARG(cons_app(s, s)) -> c14(APP(s, s), ENCARG(s)) ENCARG(cons_app(f, s)) -> c14(APP(f, s), ENCARG(f)) ENCARG(cons_app(map, s)) -> c14(APP(map, s), ENCARG(map)) ENCARG(cons_app(cons, s)) -> c14(APP(cons, s), ENCARG(cons)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, le)) -> c14(APP(encArg(x0), le), ENCARG(x0)) by ENCARG(cons_app(minus, le)) -> c14(APP(minus, le), ENCARG(minus)) ENCARG(cons_app(0, le)) -> c14(APP(0, le), ENCARG(0)) ENCARG(cons_app(s, le)) -> c14(APP(s, le), ENCARG(s)) ENCARG(cons_app(le, le)) -> c14(APP(le, le), ENCARG(le)) ENCARG(cons_app(true, le)) -> c14(APP(true, le), ENCARG(true)) ENCARG(cons_app(false, le)) -> c14(APP(false, le), ENCARG(false)) ENCARG(cons_app(if, le)) -> c14(APP(if, le), ENCARG(if)) ENCARG(cons_app(perfectp, le)) -> c14(APP(perfectp, le), ENCARG(perfectp)) ENCARG(cons_app(f, le)) -> c14(APP(f, le), ENCARG(f)) ENCARG(cons_app(map, le)) -> c14(APP(map, le), ENCARG(map)) ENCARG(cons_app(nil, le)) -> c14(APP(nil, le), ENCARG(nil)) ENCARG(cons_app(cons, le)) -> c14(APP(cons, le), ENCARG(cons)) ENCARG(cons_app(filter, le)) -> c14(APP(filter, le), ENCARG(filter)) ENCARG(cons_app(filter2, le)) -> c14(APP(filter2, le), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), le)) -> c14(APP(app(encArg(z0), encArg(z1)), le), ENCARG(cons_app(z0, z1))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, le)) -> c14(APP(minus, le), ENCARG(minus)) ENCARG(cons_app(0, le)) -> c14(APP(0, le), ENCARG(0)) ENCARG(cons_app(s, le)) -> c14(APP(s, le), ENCARG(s)) ENCARG(cons_app(le, le)) -> c14(APP(le, le), ENCARG(le)) ENCARG(cons_app(true, le)) -> c14(APP(true, le), ENCARG(true)) ENCARG(cons_app(false, le)) -> c14(APP(false, le), ENCARG(false)) ENCARG(cons_app(if, le)) -> c14(APP(if, le), ENCARG(if)) ENCARG(cons_app(perfectp, le)) -> c14(APP(perfectp, le), ENCARG(perfectp)) ENCARG(cons_app(f, le)) -> c14(APP(f, le), ENCARG(f)) ENCARG(cons_app(map, le)) -> c14(APP(map, le), ENCARG(map)) ENCARG(cons_app(nil, le)) -> c14(APP(nil, le), ENCARG(nil)) ENCARG(cons_app(cons, le)) -> c14(APP(cons, le), ENCARG(cons)) ENCARG(cons_app(filter, le)) -> c14(APP(filter, le), ENCARG(filter)) ENCARG(cons_app(filter2, le)) -> c14(APP(filter2, le), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(nil, le)) -> c14(APP(nil, le), ENCARG(nil)) ENCARG(cons_app(minus, le)) -> c14(APP(minus, le), ENCARG(minus)) ENCARG(cons_app(false, le)) -> c14(APP(false, le), ENCARG(false)) ENCARG(cons_app(f, le)) -> c14(APP(f, le), ENCARG(f)) ENCARG(cons_app(true, le)) -> c14(APP(true, le), ENCARG(true)) ENCARG(cons_app(0, le)) -> c14(APP(0, le), ENCARG(0)) ENCARG(cons_app(s, le)) -> c14(APP(s, le), ENCARG(s)) ENCARG(cons_app(filter, le)) -> c14(APP(filter, le), ENCARG(filter)) ENCARG(cons_app(perfectp, le)) -> c14(APP(perfectp, le), ENCARG(perfectp)) ENCARG(cons_app(le, le)) -> c14(APP(le, le), ENCARG(le)) ENCARG(cons_app(cons, le)) -> c14(APP(cons, le), ENCARG(cons)) ENCARG(cons_app(map, le)) -> c14(APP(map, le), ENCARG(map)) ENCARG(cons_app(if, le)) -> c14(APP(if, le), ENCARG(if)) ENCARG(cons_app(filter2, le)) -> c14(APP(filter2, le), ENCARG(filter2)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, true)) -> c14(APP(encArg(x0), true), ENCARG(x0)) by ENCARG(cons_app(minus, true)) -> c14(APP(minus, true), ENCARG(minus)) ENCARG(cons_app(0, true)) -> c14(APP(0, true), ENCARG(0)) ENCARG(cons_app(s, true)) -> c14(APP(s, true), ENCARG(s)) ENCARG(cons_app(le, true)) -> c14(APP(le, true), ENCARG(le)) ENCARG(cons_app(true, true)) -> c14(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c14(APP(false, true), ENCARG(false)) ENCARG(cons_app(if, true)) -> c14(APP(if, true), ENCARG(if)) ENCARG(cons_app(perfectp, true)) -> c14(APP(perfectp, true), ENCARG(perfectp)) ENCARG(cons_app(f, true)) -> c14(APP(f, true), ENCARG(f)) ENCARG(cons_app(map, true)) -> c14(APP(map, true), ENCARG(map)) ENCARG(cons_app(nil, true)) -> c14(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c14(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(filter, true)) -> c14(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(filter2, true)) -> c14(APP(filter2, true), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), true)) -> c14(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, true)) -> c14(APP(minus, true), ENCARG(minus)) ENCARG(cons_app(0, true)) -> c14(APP(0, true), ENCARG(0)) ENCARG(cons_app(s, true)) -> c14(APP(s, true), ENCARG(s)) ENCARG(cons_app(le, true)) -> c14(APP(le, true), ENCARG(le)) ENCARG(cons_app(true, true)) -> c14(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c14(APP(false, true), ENCARG(false)) ENCARG(cons_app(if, true)) -> c14(APP(if, true), ENCARG(if)) ENCARG(cons_app(perfectp, true)) -> c14(APP(perfectp, true), ENCARG(perfectp)) ENCARG(cons_app(f, true)) -> c14(APP(f, true), ENCARG(f)) ENCARG(cons_app(map, true)) -> c14(APP(map, true), ENCARG(map)) ENCARG(cons_app(nil, true)) -> c14(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c14(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(filter, true)) -> c14(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(filter2, true)) -> c14(APP(filter2, true), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(s, true)) -> c14(APP(s, true), ENCARG(s)) ENCARG(cons_app(false, true)) -> c14(APP(false, true), ENCARG(false)) ENCARG(cons_app(filter, true)) -> c14(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(if, true)) -> c14(APP(if, true), ENCARG(if)) ENCARG(cons_app(minus, true)) -> c14(APP(minus, true), ENCARG(minus)) ENCARG(cons_app(nil, true)) -> c14(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(true, true)) -> c14(APP(true, true), ENCARG(true)) ENCARG(cons_app(cons, true)) -> c14(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(f, true)) -> c14(APP(f, true), ENCARG(f)) ENCARG(cons_app(0, true)) -> c14(APP(0, true), ENCARG(0)) ENCARG(cons_app(map, true)) -> c14(APP(map, true), ENCARG(map)) ENCARG(cons_app(perfectp, true)) -> c14(APP(perfectp, true), ENCARG(perfectp)) ENCARG(cons_app(le, true)) -> c14(APP(le, true), ENCARG(le)) ENCARG(cons_app(filter2, true)) -> c14(APP(filter2, true), ENCARG(filter2)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, false)) -> c14(APP(encArg(x0), false), ENCARG(x0)) by ENCARG(cons_app(minus, false)) -> c14(APP(minus, false), ENCARG(minus)) ENCARG(cons_app(0, false)) -> c14(APP(0, false), ENCARG(0)) ENCARG(cons_app(s, false)) -> c14(APP(s, false), ENCARG(s)) ENCARG(cons_app(le, false)) -> c14(APP(le, false), ENCARG(le)) ENCARG(cons_app(true, false)) -> c14(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c14(APP(false, false), ENCARG(false)) ENCARG(cons_app(if, false)) -> c14(APP(if, false), ENCARG(if)) ENCARG(cons_app(perfectp, false)) -> c14(APP(perfectp, false), ENCARG(perfectp)) ENCARG(cons_app(f, false)) -> c14(APP(f, false), ENCARG(f)) ENCARG(cons_app(map, false)) -> c14(APP(map, false), ENCARG(map)) ENCARG(cons_app(nil, false)) -> c14(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c14(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(filter, false)) -> c14(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(filter2, false)) -> c14(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), false)) -> c14(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, false)) -> c14(APP(minus, false), ENCARG(minus)) ENCARG(cons_app(0, false)) -> c14(APP(0, false), ENCARG(0)) ENCARG(cons_app(s, false)) -> c14(APP(s, false), ENCARG(s)) ENCARG(cons_app(le, false)) -> c14(APP(le, false), ENCARG(le)) ENCARG(cons_app(true, false)) -> c14(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c14(APP(false, false), ENCARG(false)) ENCARG(cons_app(if, false)) -> c14(APP(if, false), ENCARG(if)) ENCARG(cons_app(perfectp, false)) -> c14(APP(perfectp, false), ENCARG(perfectp)) ENCARG(cons_app(f, false)) -> c14(APP(f, false), ENCARG(f)) ENCARG(cons_app(map, false)) -> c14(APP(map, false), ENCARG(map)) ENCARG(cons_app(nil, false)) -> c14(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c14(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(filter, false)) -> c14(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(filter2, false)) -> c14(APP(filter2, false), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(map, false)) -> c14(APP(map, false), ENCARG(map)) ENCARG(cons_app(nil, false)) -> c14(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(filter, false)) -> c14(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(0, false)) -> c14(APP(0, false), ENCARG(0)) ENCARG(cons_app(perfectp, false)) -> c14(APP(perfectp, false), ENCARG(perfectp)) ENCARG(cons_app(le, false)) -> c14(APP(le, false), ENCARG(le)) ENCARG(cons_app(true, false)) -> c14(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c14(APP(false, false), ENCARG(false)) ENCARG(cons_app(cons, false)) -> c14(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(filter2, false)) -> c14(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(s, false)) -> c14(APP(s, false), ENCARG(s)) ENCARG(cons_app(if, false)) -> c14(APP(if, false), ENCARG(if)) ENCARG(cons_app(f, false)) -> c14(APP(f, false), ENCARG(f)) ENCARG(cons_app(minus, false)) -> c14(APP(minus, false), ENCARG(minus)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, if)) -> c14(APP(encArg(x0), if), ENCARG(x0)) by ENCARG(cons_app(minus, if)) -> c14(APP(minus, if), ENCARG(minus)) ENCARG(cons_app(0, if)) -> c14(APP(0, if), ENCARG(0)) ENCARG(cons_app(s, if)) -> c14(APP(s, if), ENCARG(s)) ENCARG(cons_app(le, if)) -> c14(APP(le, if), ENCARG(le)) ENCARG(cons_app(true, if)) -> c14(APP(true, if), ENCARG(true)) ENCARG(cons_app(false, if)) -> c14(APP(false, if), ENCARG(false)) ENCARG(cons_app(if, if)) -> c14(APP(if, if), ENCARG(if)) ENCARG(cons_app(perfectp, if)) -> c14(APP(perfectp, if), ENCARG(perfectp)) ENCARG(cons_app(f, if)) -> c14(APP(f, if), ENCARG(f)) ENCARG(cons_app(map, if)) -> c14(APP(map, if), ENCARG(map)) ENCARG(cons_app(nil, if)) -> c14(APP(nil, if), ENCARG(nil)) ENCARG(cons_app(cons, if)) -> c14(APP(cons, if), ENCARG(cons)) ENCARG(cons_app(filter, if)) -> c14(APP(filter, if), ENCARG(filter)) ENCARG(cons_app(filter2, if)) -> c14(APP(filter2, if), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), if)) -> c14(APP(app(encArg(z0), encArg(z1)), if), ENCARG(cons_app(z0, z1))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, if)) -> c14(APP(minus, if), ENCARG(minus)) ENCARG(cons_app(0, if)) -> c14(APP(0, if), ENCARG(0)) ENCARG(cons_app(s, if)) -> c14(APP(s, if), ENCARG(s)) ENCARG(cons_app(le, if)) -> c14(APP(le, if), ENCARG(le)) ENCARG(cons_app(true, if)) -> c14(APP(true, if), ENCARG(true)) ENCARG(cons_app(false, if)) -> c14(APP(false, if), ENCARG(false)) ENCARG(cons_app(if, if)) -> c14(APP(if, if), ENCARG(if)) ENCARG(cons_app(perfectp, if)) -> c14(APP(perfectp, if), ENCARG(perfectp)) ENCARG(cons_app(f, if)) -> c14(APP(f, if), ENCARG(f)) ENCARG(cons_app(map, if)) -> c14(APP(map, if), ENCARG(map)) ENCARG(cons_app(nil, if)) -> c14(APP(nil, if), ENCARG(nil)) ENCARG(cons_app(cons, if)) -> c14(APP(cons, if), ENCARG(cons)) ENCARG(cons_app(filter, if)) -> c14(APP(filter, if), ENCARG(filter)) ENCARG(cons_app(filter2, if)) -> c14(APP(filter2, if), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(filter, if)) -> c14(APP(filter, if), ENCARG(filter)) ENCARG(cons_app(nil, if)) -> c14(APP(nil, if), ENCARG(nil)) ENCARG(cons_app(filter2, if)) -> c14(APP(filter2, if), ENCARG(filter2)) ENCARG(cons_app(cons, if)) -> c14(APP(cons, if), ENCARG(cons)) ENCARG(cons_app(map, if)) -> c14(APP(map, if), ENCARG(map)) ENCARG(cons_app(f, if)) -> c14(APP(f, if), ENCARG(f)) ENCARG(cons_app(true, if)) -> c14(APP(true, if), ENCARG(true)) ENCARG(cons_app(perfectp, if)) -> c14(APP(perfectp, if), ENCARG(perfectp)) ENCARG(cons_app(if, if)) -> c14(APP(if, if), ENCARG(if)) ENCARG(cons_app(le, if)) -> c14(APP(le, if), ENCARG(le)) ENCARG(cons_app(false, if)) -> c14(APP(false, if), ENCARG(false)) ENCARG(cons_app(s, if)) -> c14(APP(s, if), ENCARG(s)) ENCARG(cons_app(0, if)) -> c14(APP(0, if), ENCARG(0)) ENCARG(cons_app(minus, if)) -> c14(APP(minus, if), ENCARG(minus)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, perfectp)) -> c14(APP(encArg(x0), perfectp), ENCARG(x0)) by ENCARG(cons_app(minus, perfectp)) -> c14(APP(minus, perfectp), ENCARG(minus)) ENCARG(cons_app(0, perfectp)) -> c14(APP(0, perfectp), ENCARG(0)) ENCARG(cons_app(s, perfectp)) -> c14(APP(s, perfectp), ENCARG(s)) ENCARG(cons_app(le, perfectp)) -> c14(APP(le, perfectp), ENCARG(le)) ENCARG(cons_app(true, perfectp)) -> c14(APP(true, perfectp), ENCARG(true)) ENCARG(cons_app(false, perfectp)) -> c14(APP(false, perfectp), ENCARG(false)) ENCARG(cons_app(if, perfectp)) -> c14(APP(if, perfectp), ENCARG(if)) ENCARG(cons_app(perfectp, perfectp)) -> c14(APP(perfectp, perfectp), ENCARG(perfectp)) ENCARG(cons_app(f, perfectp)) -> c14(APP(f, perfectp), ENCARG(f)) ENCARG(cons_app(map, perfectp)) -> c14(APP(map, perfectp), ENCARG(map)) ENCARG(cons_app(nil, perfectp)) -> c14(APP(nil, perfectp), ENCARG(nil)) ENCARG(cons_app(cons, perfectp)) -> c14(APP(cons, perfectp), ENCARG(cons)) ENCARG(cons_app(filter, perfectp)) -> c14(APP(filter, perfectp), ENCARG(filter)) ENCARG(cons_app(filter2, perfectp)) -> c14(APP(filter2, perfectp), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), perfectp)) -> c14(APP(app(encArg(z0), encArg(z1)), perfectp), ENCARG(cons_app(z0, z1))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, perfectp)) -> c14(APP(minus, perfectp), ENCARG(minus)) ENCARG(cons_app(0, perfectp)) -> c14(APP(0, perfectp), ENCARG(0)) ENCARG(cons_app(s, perfectp)) -> c14(APP(s, perfectp), ENCARG(s)) ENCARG(cons_app(le, perfectp)) -> c14(APP(le, perfectp), ENCARG(le)) ENCARG(cons_app(true, perfectp)) -> c14(APP(true, perfectp), ENCARG(true)) ENCARG(cons_app(false, perfectp)) -> c14(APP(false, perfectp), ENCARG(false)) ENCARG(cons_app(if, perfectp)) -> c14(APP(if, perfectp), ENCARG(if)) ENCARG(cons_app(perfectp, perfectp)) -> c14(APP(perfectp, perfectp), ENCARG(perfectp)) ENCARG(cons_app(f, perfectp)) -> c14(APP(f, perfectp), ENCARG(f)) ENCARG(cons_app(map, perfectp)) -> c14(APP(map, perfectp), ENCARG(map)) ENCARG(cons_app(nil, perfectp)) -> c14(APP(nil, perfectp), ENCARG(nil)) ENCARG(cons_app(cons, perfectp)) -> c14(APP(cons, perfectp), ENCARG(cons)) ENCARG(cons_app(filter, perfectp)) -> c14(APP(filter, perfectp), ENCARG(filter)) ENCARG(cons_app(filter2, perfectp)) -> c14(APP(filter2, perfectp), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(nil, perfectp)) -> c14(APP(nil, perfectp), ENCARG(nil)) ENCARG(cons_app(map, perfectp)) -> c14(APP(map, perfectp), ENCARG(map)) ENCARG(cons_app(cons, perfectp)) -> c14(APP(cons, perfectp), ENCARG(cons)) ENCARG(cons_app(false, perfectp)) -> c14(APP(false, perfectp), ENCARG(false)) ENCARG(cons_app(f, perfectp)) -> c14(APP(f, perfectp), ENCARG(f)) ENCARG(cons_app(s, perfectp)) -> c14(APP(s, perfectp), ENCARG(s)) ENCARG(cons_app(filter2, perfectp)) -> c14(APP(filter2, perfectp), ENCARG(filter2)) ENCARG(cons_app(if, perfectp)) -> c14(APP(if, perfectp), ENCARG(if)) ENCARG(cons_app(filter, perfectp)) -> c14(APP(filter, perfectp), ENCARG(filter)) ENCARG(cons_app(minus, perfectp)) -> c14(APP(minus, perfectp), ENCARG(minus)) ENCARG(cons_app(perfectp, perfectp)) -> c14(APP(perfectp, perfectp), ENCARG(perfectp)) ENCARG(cons_app(le, perfectp)) -> c14(APP(le, perfectp), ENCARG(le)) ENCARG(cons_app(0, perfectp)) -> c14(APP(0, perfectp), ENCARG(0)) ENCARG(cons_app(true, perfectp)) -> c14(APP(true, perfectp), ENCARG(true)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, f)) -> c14(APP(encArg(x0), f), ENCARG(x0)) by ENCARG(cons_app(minus, f)) -> c14(APP(minus, f), ENCARG(minus)) ENCARG(cons_app(0, f)) -> c14(APP(0, f), ENCARG(0)) ENCARG(cons_app(s, f)) -> c14(APP(s, f), ENCARG(s)) ENCARG(cons_app(le, f)) -> c14(APP(le, f), ENCARG(le)) ENCARG(cons_app(true, f)) -> c14(APP(true, f), ENCARG(true)) ENCARG(cons_app(false, f)) -> c14(APP(false, f), ENCARG(false)) ENCARG(cons_app(if, f)) -> c14(APP(if, f), ENCARG(if)) ENCARG(cons_app(perfectp, f)) -> c14(APP(perfectp, f), ENCARG(perfectp)) ENCARG(cons_app(f, f)) -> c14(APP(f, f), ENCARG(f)) ENCARG(cons_app(map, f)) -> c14(APP(map, f), ENCARG(map)) ENCARG(cons_app(nil, f)) -> c14(APP(nil, f), ENCARG(nil)) ENCARG(cons_app(cons, f)) -> c14(APP(cons, f), ENCARG(cons)) ENCARG(cons_app(filter, f)) -> c14(APP(filter, f), ENCARG(filter)) ENCARG(cons_app(filter2, f)) -> c14(APP(filter2, f), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), f)) -> c14(APP(app(encArg(z0), encArg(z1)), f), ENCARG(cons_app(z0, z1))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, f)) -> c14(APP(minus, f), ENCARG(minus)) ENCARG(cons_app(0, f)) -> c14(APP(0, f), ENCARG(0)) ENCARG(cons_app(s, f)) -> c14(APP(s, f), ENCARG(s)) ENCARG(cons_app(le, f)) -> c14(APP(le, f), ENCARG(le)) ENCARG(cons_app(true, f)) -> c14(APP(true, f), ENCARG(true)) ENCARG(cons_app(false, f)) -> c14(APP(false, f), ENCARG(false)) ENCARG(cons_app(if, f)) -> c14(APP(if, f), ENCARG(if)) ENCARG(cons_app(perfectp, f)) -> c14(APP(perfectp, f), ENCARG(perfectp)) ENCARG(cons_app(f, f)) -> c14(APP(f, f), ENCARG(f)) ENCARG(cons_app(map, f)) -> c14(APP(map, f), ENCARG(map)) ENCARG(cons_app(nil, f)) -> c14(APP(nil, f), ENCARG(nil)) ENCARG(cons_app(cons, f)) -> c14(APP(cons, f), ENCARG(cons)) ENCARG(cons_app(filter, f)) -> c14(APP(filter, f), ENCARG(filter)) ENCARG(cons_app(filter2, f)) -> c14(APP(filter2, f), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(perfectp, f)) -> c14(APP(perfectp, f), ENCARG(perfectp)) ENCARG(cons_app(if, f)) -> c14(APP(if, f), ENCARG(if)) ENCARG(cons_app(le, f)) -> c14(APP(le, f), ENCARG(le)) ENCARG(cons_app(true, f)) -> c14(APP(true, f), ENCARG(true)) ENCARG(cons_app(0, f)) -> c14(APP(0, f), ENCARG(0)) ENCARG(cons_app(s, f)) -> c14(APP(s, f), ENCARG(s)) ENCARG(cons_app(minus, f)) -> c14(APP(minus, f), ENCARG(minus)) ENCARG(cons_app(filter, f)) -> c14(APP(filter, f), ENCARG(filter)) ENCARG(cons_app(map, f)) -> c14(APP(map, f), ENCARG(map)) ENCARG(cons_app(f, f)) -> c14(APP(f, f), ENCARG(f)) ENCARG(cons_app(nil, f)) -> c14(APP(nil, f), ENCARG(nil)) ENCARG(cons_app(filter2, f)) -> c14(APP(filter2, f), ENCARG(filter2)) ENCARG(cons_app(false, f)) -> c14(APP(false, f), ENCARG(false)) ENCARG(cons_app(cons, f)) -> c14(APP(cons, f), ENCARG(cons)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, map)) -> c14(APP(encArg(x0), map), ENCARG(x0)) by ENCARG(cons_app(minus, map)) -> c14(APP(minus, map), ENCARG(minus)) ENCARG(cons_app(0, map)) -> c14(APP(0, map), ENCARG(0)) ENCARG(cons_app(s, map)) -> c14(APP(s, map), ENCARG(s)) ENCARG(cons_app(le, map)) -> c14(APP(le, map), ENCARG(le)) ENCARG(cons_app(true, map)) -> c14(APP(true, map), ENCARG(true)) ENCARG(cons_app(false, map)) -> c14(APP(false, map), ENCARG(false)) ENCARG(cons_app(if, map)) -> c14(APP(if, map), ENCARG(if)) ENCARG(cons_app(perfectp, map)) -> c14(APP(perfectp, map), ENCARG(perfectp)) ENCARG(cons_app(f, map)) -> c14(APP(f, map), ENCARG(f)) ENCARG(cons_app(map, map)) -> c14(APP(map, map), ENCARG(map)) ENCARG(cons_app(nil, map)) -> c14(APP(nil, map), ENCARG(nil)) ENCARG(cons_app(cons, map)) -> c14(APP(cons, map), ENCARG(cons)) ENCARG(cons_app(filter, map)) -> c14(APP(filter, map), ENCARG(filter)) ENCARG(cons_app(filter2, map)) -> c14(APP(filter2, map), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), map)) -> c14(APP(app(encArg(z0), encArg(z1)), map), ENCARG(cons_app(z0, z1))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, map)) -> c14(APP(minus, map), ENCARG(minus)) ENCARG(cons_app(0, map)) -> c14(APP(0, map), ENCARG(0)) ENCARG(cons_app(s, map)) -> c14(APP(s, map), ENCARG(s)) ENCARG(cons_app(le, map)) -> c14(APP(le, map), ENCARG(le)) ENCARG(cons_app(true, map)) -> c14(APP(true, map), ENCARG(true)) ENCARG(cons_app(false, map)) -> c14(APP(false, map), ENCARG(false)) ENCARG(cons_app(if, map)) -> c14(APP(if, map), ENCARG(if)) ENCARG(cons_app(perfectp, map)) -> c14(APP(perfectp, map), ENCARG(perfectp)) ENCARG(cons_app(f, map)) -> c14(APP(f, map), ENCARG(f)) ENCARG(cons_app(map, map)) -> c14(APP(map, map), ENCARG(map)) ENCARG(cons_app(nil, map)) -> c14(APP(nil, map), ENCARG(nil)) ENCARG(cons_app(cons, map)) -> c14(APP(cons, map), ENCARG(cons)) ENCARG(cons_app(filter, map)) -> c14(APP(filter, map), ENCARG(filter)) ENCARG(cons_app(filter2, map)) -> c14(APP(filter2, map), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(filter, map)) -> c14(APP(filter, map), ENCARG(filter)) ENCARG(cons_app(perfectp, map)) -> c14(APP(perfectp, map), ENCARG(perfectp)) ENCARG(cons_app(le, map)) -> c14(APP(le, map), ENCARG(le)) ENCARG(cons_app(if, map)) -> c14(APP(if, map), ENCARG(if)) ENCARG(cons_app(s, map)) -> c14(APP(s, map), ENCARG(s)) ENCARG(cons_app(true, map)) -> c14(APP(true, map), ENCARG(true)) ENCARG(cons_app(false, map)) -> c14(APP(false, map), ENCARG(false)) ENCARG(cons_app(0, map)) -> c14(APP(0, map), ENCARG(0)) ENCARG(cons_app(filter2, map)) -> c14(APP(filter2, map), ENCARG(filter2)) ENCARG(cons_app(minus, map)) -> c14(APP(minus, map), ENCARG(minus)) ENCARG(cons_app(map, map)) -> c14(APP(map, map), ENCARG(map)) ENCARG(cons_app(nil, map)) -> c14(APP(nil, map), ENCARG(nil)) ENCARG(cons_app(cons, map)) -> c14(APP(cons, map), ENCARG(cons)) ENCARG(cons_app(f, map)) -> c14(APP(f, map), ENCARG(f)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c14(APP(encArg(x0), nil), ENCARG(x0)) by ENCARG(cons_app(minus, nil)) -> c14(APP(minus, nil), ENCARG(minus)) ENCARG(cons_app(0, nil)) -> c14(APP(0, nil), ENCARG(0)) ENCARG(cons_app(s, nil)) -> c14(APP(s, nil), ENCARG(s)) ENCARG(cons_app(le, nil)) -> c14(APP(le, nil), ENCARG(le)) ENCARG(cons_app(true, nil)) -> c14(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c14(APP(false, nil), ENCARG(false)) ENCARG(cons_app(if, nil)) -> c14(APP(if, nil), ENCARG(if)) ENCARG(cons_app(perfectp, nil)) -> c14(APP(perfectp, nil), ENCARG(perfectp)) ENCARG(cons_app(f, nil)) -> c14(APP(f, nil), ENCARG(f)) ENCARG(cons_app(map, nil)) -> c14(APP(map, nil), ENCARG(map)) ENCARG(cons_app(nil, nil)) -> c14(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c14(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(filter, nil)) -> c14(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(filter2, nil)) -> c14(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), nil)) -> c14(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, nil)) -> c14(APP(minus, nil), ENCARG(minus)) ENCARG(cons_app(0, nil)) -> c14(APP(0, nil), ENCARG(0)) ENCARG(cons_app(s, nil)) -> c14(APP(s, nil), ENCARG(s)) ENCARG(cons_app(le, nil)) -> c14(APP(le, nil), ENCARG(le)) ENCARG(cons_app(true, nil)) -> c14(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c14(APP(false, nil), ENCARG(false)) ENCARG(cons_app(if, nil)) -> c14(APP(if, nil), ENCARG(if)) ENCARG(cons_app(perfectp, nil)) -> c14(APP(perfectp, nil), ENCARG(perfectp)) ENCARG(cons_app(f, nil)) -> c14(APP(f, nil), ENCARG(f)) ENCARG(cons_app(map, nil)) -> c14(APP(map, nil), ENCARG(map)) ENCARG(cons_app(nil, nil)) -> c14(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c14(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(filter, nil)) -> c14(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(filter2, nil)) -> c14(APP(filter2, nil), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(perfectp, nil)) -> c14(APP(perfectp, nil), ENCARG(perfectp)) ENCARG(cons_app(le, nil)) -> c14(APP(le, nil), ENCARG(le)) ENCARG(cons_app(s, nil)) -> c14(APP(s, nil), ENCARG(s)) ENCARG(cons_app(if, nil)) -> c14(APP(if, nil), ENCARG(if)) ENCARG(cons_app(true, nil)) -> c14(APP(true, nil), ENCARG(true)) ENCARG(cons_app(0, nil)) -> c14(APP(0, nil), ENCARG(0)) ENCARG(cons_app(minus, nil)) -> c14(APP(minus, nil), ENCARG(minus)) ENCARG(cons_app(f, nil)) -> c14(APP(f, nil), ENCARG(f)) ENCARG(cons_app(false, nil)) -> c14(APP(false, nil), ENCARG(false)) ENCARG(cons_app(filter, nil)) -> c14(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(map, nil)) -> c14(APP(map, nil), ENCARG(map)) ENCARG(cons_app(filter2, nil)) -> c14(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(cons, nil)) -> c14(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(nil, nil)) -> c14(APP(nil, nil), ENCARG(nil)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c14(APP(encArg(x0), cons), ENCARG(x0)) by ENCARG(cons_app(minus, cons)) -> c14(APP(minus, cons), ENCARG(minus)) ENCARG(cons_app(0, cons)) -> c14(APP(0, cons), ENCARG(0)) ENCARG(cons_app(s, cons)) -> c14(APP(s, cons), ENCARG(s)) ENCARG(cons_app(le, cons)) -> c14(APP(le, cons), ENCARG(le)) ENCARG(cons_app(true, cons)) -> c14(APP(true, cons), ENCARG(true)) ENCARG(cons_app(false, cons)) -> c14(APP(false, cons), ENCARG(false)) ENCARG(cons_app(if, cons)) -> c14(APP(if, cons), ENCARG(if)) ENCARG(cons_app(perfectp, cons)) -> c14(APP(perfectp, cons), ENCARG(perfectp)) ENCARG(cons_app(f, cons)) -> c14(APP(f, cons), ENCARG(f)) ENCARG(cons_app(map, cons)) -> c14(APP(map, cons), ENCARG(map)) ENCARG(cons_app(nil, cons)) -> c14(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c14(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(filter, cons)) -> c14(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(filter2, cons)) -> c14(APP(filter2, cons), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), cons)) -> c14(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, cons)) -> c14(APP(minus, cons), ENCARG(minus)) ENCARG(cons_app(0, cons)) -> c14(APP(0, cons), ENCARG(0)) ENCARG(cons_app(s, cons)) -> c14(APP(s, cons), ENCARG(s)) ENCARG(cons_app(le, cons)) -> c14(APP(le, cons), ENCARG(le)) ENCARG(cons_app(true, cons)) -> c14(APP(true, cons), ENCARG(true)) ENCARG(cons_app(false, cons)) -> c14(APP(false, cons), ENCARG(false)) ENCARG(cons_app(if, cons)) -> c14(APP(if, cons), ENCARG(if)) ENCARG(cons_app(perfectp, cons)) -> c14(APP(perfectp, cons), ENCARG(perfectp)) ENCARG(cons_app(f, cons)) -> c14(APP(f, cons), ENCARG(f)) ENCARG(cons_app(map, cons)) -> c14(APP(map, cons), ENCARG(map)) ENCARG(cons_app(nil, cons)) -> c14(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c14(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(filter, cons)) -> c14(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(filter2, cons)) -> c14(APP(filter2, cons), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(0, cons)) -> c14(APP(0, cons), ENCARG(0)) ENCARG(cons_app(true, cons)) -> c14(APP(true, cons), ENCARG(true)) ENCARG(cons_app(perfectp, cons)) -> c14(APP(perfectp, cons), ENCARG(perfectp)) ENCARG(cons_app(le, cons)) -> c14(APP(le, cons), ENCARG(le)) ENCARG(cons_app(nil, cons)) -> c14(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(f, cons)) -> c14(APP(f, cons), ENCARG(f)) ENCARG(cons_app(s, cons)) -> c14(APP(s, cons), ENCARG(s)) ENCARG(cons_app(filter2, cons)) -> c14(APP(filter2, cons), ENCARG(filter2)) ENCARG(cons_app(map, cons)) -> c14(APP(map, cons), ENCARG(map)) ENCARG(cons_app(cons, cons)) -> c14(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(minus, cons)) -> c14(APP(minus, cons), ENCARG(minus)) ENCARG(cons_app(false, cons)) -> c14(APP(false, cons), ENCARG(false)) ENCARG(cons_app(filter, cons)) -> c14(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(if, cons)) -> c14(APP(if, cons), ENCARG(if)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, filter)) -> c14(APP(encArg(x0), filter), ENCARG(x0)) by ENCARG(cons_app(minus, filter)) -> c14(APP(minus, filter), ENCARG(minus)) ENCARG(cons_app(0, filter)) -> c14(APP(0, filter), ENCARG(0)) ENCARG(cons_app(s, filter)) -> c14(APP(s, filter), ENCARG(s)) ENCARG(cons_app(le, filter)) -> c14(APP(le, filter), ENCARG(le)) ENCARG(cons_app(true, filter)) -> c14(APP(true, filter), ENCARG(true)) ENCARG(cons_app(false, filter)) -> c14(APP(false, filter), ENCARG(false)) ENCARG(cons_app(if, filter)) -> c14(APP(if, filter), ENCARG(if)) ENCARG(cons_app(perfectp, filter)) -> c14(APP(perfectp, filter), ENCARG(perfectp)) ENCARG(cons_app(f, filter)) -> c14(APP(f, filter), ENCARG(f)) ENCARG(cons_app(map, filter)) -> c14(APP(map, filter), ENCARG(map)) ENCARG(cons_app(nil, filter)) -> c14(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(cons, filter)) -> c14(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(filter, filter)) -> c14(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(filter2, filter)) -> c14(APP(filter2, filter), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), filter)) -> c14(APP(app(encArg(z0), encArg(z1)), filter), ENCARG(cons_app(z0, z1))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) ENCARG(cons_app(minus, filter)) -> c14(APP(minus, filter), ENCARG(minus)) ENCARG(cons_app(0, filter)) -> c14(APP(0, filter), ENCARG(0)) ENCARG(cons_app(s, filter)) -> c14(APP(s, filter), ENCARG(s)) ENCARG(cons_app(le, filter)) -> c14(APP(le, filter), ENCARG(le)) ENCARG(cons_app(true, filter)) -> c14(APP(true, filter), ENCARG(true)) ENCARG(cons_app(false, filter)) -> c14(APP(false, filter), ENCARG(false)) ENCARG(cons_app(if, filter)) -> c14(APP(if, filter), ENCARG(if)) ENCARG(cons_app(perfectp, filter)) -> c14(APP(perfectp, filter), ENCARG(perfectp)) ENCARG(cons_app(f, filter)) -> c14(APP(f, filter), ENCARG(f)) ENCARG(cons_app(map, filter)) -> c14(APP(map, filter), ENCARG(map)) ENCARG(cons_app(nil, filter)) -> c14(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(cons, filter)) -> c14(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(filter, filter)) -> c14(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(filter2, filter)) -> c14(APP(filter2, filter), ENCARG(filter2)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(true, filter)) -> c14(APP(true, filter), ENCARG(true)) ENCARG(cons_app(filter2, filter)) -> c14(APP(filter2, filter), ENCARG(filter2)) ENCARG(cons_app(cons, filter)) -> c14(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(f, filter)) -> c14(APP(f, filter), ENCARG(f)) ENCARG(cons_app(if, filter)) -> c14(APP(if, filter), ENCARG(if)) ENCARG(cons_app(false, filter)) -> c14(APP(false, filter), ENCARG(false)) ENCARG(cons_app(s, filter)) -> c14(APP(s, filter), ENCARG(s)) ENCARG(cons_app(0, filter)) -> c14(APP(0, filter), ENCARG(0)) ENCARG(cons_app(nil, filter)) -> c14(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(minus, filter)) -> c14(APP(minus, filter), ENCARG(minus)) ENCARG(cons_app(filter, filter)) -> c14(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(map, filter)) -> c14(APP(map, filter), ENCARG(map)) ENCARG(cons_app(perfectp, filter)) -> c14(APP(perfectp, filter), ENCARG(perfectp)) ENCARG(cons_app(le, filter)) -> c14(APP(le, filter), ENCARG(le)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(minus) -> minus encArg(0) -> 0 encArg(s) -> s encArg(le) -> le encArg(true) -> true encArg(false) -> false encArg(if) -> if encArg(perfectp) -> perfectp encArg(f) -> f encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(minus, 0), z0) -> 0 app(app(minus, app(s, z0)), 0) -> app(s, z0) app(app(minus, app(s, z0)), app(s, z1)) -> app(app(minus, z0), z1) app(app(le, 0), z0) -> true app(app(le, app(s, z0)), 0) -> false app(app(le, app(s, z0)), app(s, z1)) -> app(app(le, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(perfectp, 0) -> false app(perfectp, app(s, z0)) -> app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0)) app(app(app(app(f, 0), z0), 0), z1) -> true app(app(app(app(f, 0), z0), app(s, z1)), z2) -> false app(app(app(app(f, app(s, z0)), 0), z1), z2) -> app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2) app(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3) -> app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter2)) -> c14(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(minus, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(le, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(perfectp, x1)) -> c14(APP(perfectp, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(f, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c14(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c14(ENCARG(x1)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, minus) -> c(APP(encArg(x0), minus)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, perfectp) -> c(APP(encArg(x0), perfectp)) ENCODE_APP(x0, f) -> c(APP(encArg(x0), f)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(perfectp, x1) -> c(APP(perfectp, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, minus))) -> c14(APP(encArg(x0), app(encArg(x1), minus)), ENCARG(x0), ENCARG(cons_app(x1, minus))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c14(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c14(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, le))) -> c14(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c14(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c14(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c14(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, perfectp))) -> c14(APP(encArg(x0), app(encArg(x1), perfectp)), ENCARG(x0), ENCARG(cons_app(x1, perfectp))) ENCARG(cons_app(x0, cons_app(x1, f))) -> c14(APP(encArg(x0), app(encArg(x1), f)), ENCARG(x0), ENCARG(cons_app(x1, f))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c14(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c14(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c14(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c14(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c14(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c14(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(minus, x2))) -> c14(APP(encArg(x0), app(minus, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minus, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c14(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c14(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(le, x2))) -> c14(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c14(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c14(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c14(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(perfectp, x2))) -> c14(APP(encArg(x0), app(perfectp, encArg(x2))), ENCARG(x0), ENCARG(cons_app(perfectp, x2))) ENCARG(cons_app(x0, cons_app(f, x2))) -> c14(APP(encArg(x0), app(f, encArg(x2))), ENCARG(x0), ENCARG(cons_app(f, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c14(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c14(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c14(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c14(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c14(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c14(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c14(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minus, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(perfectp, cons_app(x1, x2))) -> c14(APP(perfectp, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(f, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c14(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, minus), x2)) -> c14(APP(app(encArg(x0), minus), encArg(x2)), ENCARG(cons_app(x0, minus)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c14(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c14(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c14(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c14(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c14(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c14(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, perfectp), x2)) -> c14(APP(app(encArg(x0), perfectp), encArg(x2)), ENCARG(cons_app(x0, perfectp)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, f), x2)) -> c14(APP(app(encArg(x0), f), encArg(x2)), ENCARG(cons_app(x0, f)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c14(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c14(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c14(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c14(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c14(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c14(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(minus, x1), x2)) -> c14(APP(app(minus, encArg(x1)), encArg(x2)), ENCARG(cons_app(minus, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(le, x1), x2)) -> c14(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(perfectp, x1), x2)) -> c14(APP(app(perfectp, encArg(x1)), encArg(x2)), ENCARG(cons_app(perfectp, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c14(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c14(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c14(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), minus)) -> c14(APP(app(encArg(x0), encArg(x1)), minus), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c14(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c14(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c14(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c14(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c14(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c14(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), perfectp)) -> c14(APP(app(encArg(x0), encArg(x1)), perfectp), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), f)) -> c14(APP(app(encArg(x0), encArg(x1)), f), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c14(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c14(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c14(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c14(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c14(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c14(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c14(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c14(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c14(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c14(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(f, x1), x2)) -> c14(ENCARG(cons_app(f, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c14(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c14(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c14(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(perfectp, 0)) -> c14(APP(perfectp, 0)) S tuples: APP(app(minus, 0), z0) -> c30 APP(app(le, 0), z0) -> c33 APP(app(le, app(s, z0)), 0) -> c34 APP(app(app(if, true), z0), z1) -> c36 APP(app(app(if, false), z0), z1) -> c37 APP(perfectp, 0) -> c38 APP(app(app(app(f, 0), z0), 0), z1) -> c40 APP(app(app(app(f, 0), z0), app(s, z1)), z2) -> c41 APP(app(map, z0), nil) -> c44 APP(app(filter, z0), nil) -> c46 APP(app(minus, app(s, z0)), 0) -> c31 APP(app(minus, app(s, z0)), app(s, z1)) -> c32(APP(app(minus, z0), z1)) APP(app(le, app(s, z0)), app(s, z1)) -> c35(APP(app(le, z0), z1)) APP(perfectp, app(s, z0)) -> c39(APP(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))) APP(app(app(app(f, app(s, z0)), 0), z1), z2) -> c42(APP(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2), APP(app(minus, z1), app(s, z0))) APP(app(map, z0), app(app(cons, z1), z2)) -> c45(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c48(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c49(APP(app(filter, z0), z2)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z1), 0) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0)), app(app(app(app(f, z0), 0), app(app(minus, z1), app(s, z0))), 0)), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z1), 0), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), 0), z1), 0)) APP(app(app(app(f, app(s, app(s, z0))), app(s, x1)), z2), app(s, z1)) -> c43(APP(app(app(if, app(app(le, app(s, z0)), x1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1))), app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), app(s, z1))), app(app(app(app(f, z0), app(s, z1)), z2), app(s, z1)))), APP(app(le, app(s, z0)), x1), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, x1), app(s, z0))), z2), app(s, z1)), APP(app(minus, x1), app(s, z0)), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), app(s, z1))) APP(app(app(app(f, app(s, 0)), app(s, x1)), 0), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0)), true), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), 0), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), 0), z0)) APP(app(app(app(f, app(s, 0)), app(s, x1)), app(s, z1)), z0) -> c43(APP(app(app(if, app(app(le, 0), x1)), app(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0)), false), APP(app(le, 0), x1), APP(app(app(app(f, app(s, 0)), app(app(minus, x1), 0)), app(s, z1)), z0), APP(app(minus, x1), 0), APP(app(app(app(f, 0), z0), app(s, z1)), z0)) APP(app(app(app(f, app(s, z0)), app(s, 0)), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), 0)), app(app(app(app(f, app(s, z0)), 0), x2), x3)), app(app(app(app(f, z0), x3), x2), x3)), APP(app(le, z0), 0), APP(app(app(app(f, app(s, z0)), app(app(minus, 0), z0)), x2), x3), APP(app(minus, 0), z0), APP(app(app(app(f, z0), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, 0), app(s, z0))), app(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), app(s, z0)), APP(app(app(app(f, app(s, 0)), app(app(minus, app(s, z0)), 0)), x2), x3), APP(app(minus, app(s, z0)), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z1))), app(s, app(s, z0))), x2), x3) -> c43(APP(app(app(if, app(app(le, app(s, z1)), app(s, z0))), app(app(app(app(f, app(s, app(s, z1))), app(app(minus, z0), z1)), x2), x3)), app(app(app(app(f, app(s, z1)), x3), x2), x3)), APP(app(le, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, app(s, z1))), app(app(minus, app(s, z0)), app(s, z1))), x2), x3), APP(app(minus, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, z1)), x3), x2), x3)) APP(app(app(app(f, app(s, 0)), app(s, z0)), x2), x3) -> c43(APP(app(app(if, true), app(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3)), app(app(app(app(f, 0), x3), x2), x3)), APP(app(le, 0), z0), APP(app(app(app(f, app(s, 0)), app(app(minus, z0), 0)), x2), x3), APP(app(minus, z0), 0), APP(app(app(app(f, 0), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, 0)), x2), x3) -> c43(APP(app(app(if, false), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), 0), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, 0), app(s, z0))), x2), x3), APP(app(minus, 0), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(app(app(f, app(s, app(s, z0))), app(s, app(s, z1))), x2), x3) -> c43(APP(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3)), app(app(app(app(f, app(s, z0)), x3), x2), x3)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(app(app(f, app(s, app(s, z0))), app(app(minus, app(s, z1)), app(s, z0))), x2), x3), APP(app(minus, app(s, z1)), app(s, z0)), APP(app(app(app(f, app(s, z0)), x3), x2), x3)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(minus, z0), z1)), app(minus, app(s, z0))), app(s, z1)), x2), APP(app(minus, app(s, z0)), app(s, z1))) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c47(APP(app(app(app(filter2, true), app(le, 0)), z0), x2), APP(app(le, 0), z0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), app(le, app(s, z0))), 0), x2), APP(app(le, app(s, z0)), 0)) APP(app(filter, app(le, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c47(APP(app(app(app(filter2, app(app(le, z0), z1)), app(le, app(s, z0))), app(s, z1)), x2), APP(app(le, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z0), app(app(if, true), z0)), z1), x2), APP(app(app(if, true), z0), z1)) APP(app(filter, app(app(if, false), z0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, perfectp), app(app(cons, 0), x2)) -> c47(APP(app(app(app(filter2, false), perfectp), 0), x2), APP(perfectp, 0)) APP(app(filter, perfectp), app(app(cons, app(s, z0)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), app(s, 0)), app(s, z0)), app(s, z0))), perfectp), app(s, z0)), x2), APP(perfectp, app(s, z0))) APP(app(filter, app(app(app(f, 0), z0), 0)), app(app(cons, z1), x2)) -> c47(APP(app(app(app(filter2, true), app(app(app(f, 0), z0), 0)), z1), x2), APP(app(app(app(f, 0), z0), 0), z1)) APP(app(filter, app(app(app(f, 0), z0), app(s, z1))), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, false), app(app(app(f, 0), z0), app(s, z1))), z2), x2), APP(app(app(app(f, 0), z0), app(s, z1)), z2)) APP(app(filter, app(app(app(f, app(s, z0)), 0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(f, z0), z2), app(app(minus, z1), app(s, z0))), z2)), app(app(app(f, app(s, z0)), 0), z1)), z2), x2), APP(app(app(app(f, app(s, z0)), 0), z1), z2)) APP(app(filter, app(app(app(f, app(s, z0)), app(s, z1)), z2)), app(app(cons, z3), x2)) -> c47(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(app(app(f, app(s, z0)), app(app(minus, z1), z0)), z2), z3)), app(app(app(app(f, z0), z3), z2), z3))), app(app(app(f, app(s, z0)), app(s, z1)), z2)), z3), x2), APP(app(app(app(f, app(s, z0)), app(s, z1)), z2), z3)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(minus, 0)), app(app(cons, z0), x2)) -> c47(APP(app(minus, 0), z0)) APP(app(filter, app(minus, app(s, z0))), app(app(cons, 0), x2)) -> c47(APP(app(minus, app(s, z0)), 0)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c47(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c47(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c47(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c47(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c30, c33, c34, c36, c37, c38, c40, c41, c44, c46, c31, c32_1, c35_1, c39_1, c42_2, c45_2, c48_1, c49_1, c14_2, c14_1, c43_5, c47_2, c47_1, c_1, c14_3