/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 273 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), 9 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), 87 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 11 ms] (26) CpxRNTS (27) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxRNTS (29) CompletionProof [UPPER BOUND(ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (34) CdtProblem (35) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (42) CdtProblem (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 22 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (52) CdtProblem (53) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 4 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (64) CdtProblem (65) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 96 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 33 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 196 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 18 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 18 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (88) CdtProblem (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 5 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 59 ms] (96) CdtProblem (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 53 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms] (108) CdtProblem (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (116) 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(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(eq, 0), 0) -> true app(app(eq, 0), app(s, y)) -> false app(app(eq, app(s, x)), 0) -> false app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(minsort, nil) -> nil app(minsort, app(app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) app(app(min, x), nil) -> x app(app(min, x), app(app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) app(app(del, x), nil) -> nil app(app(del, x), app(app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map 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(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(eq, 0), 0) -> true app(app(eq, 0), app(s, y)) -> false app(app(eq, app(s, x)), 0) -> false app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(minsort, nil) -> nil app(minsort, app(app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) app(app(min, x), nil) -> x app(app(min, x), app(app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) app(app(del, x), nil) -> nil app(app(del, x), app(app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map 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(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(eq, 0), 0) -> true app(app(eq, 0), app(s, y)) -> false app(app(eq, app(s, x)), 0) -> false app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(minsort, nil) -> nil app(minsort, app(app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) app(app(min, x), nil) -> x app(app(min, x), app(app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) app(app(del, x), nil) -> nil app(app(del, x), app(app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map 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(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(eq, 0), 0) -> true app(app(eq, 0), app(s, y)) -> false app(app(eq, app(s, x)), 0) -> false app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(minsort, nil) -> nil app(minsort, app(app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) app(app(min, x), nil) -> x app(app(min, x), app(app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) app(app(del, x), nil) -> nil app(app(del, x), app(app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map 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(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(eq, 0'), 0') -> true app(app(eq, 0'), app(s, y)) -> false app(app(eq, app(s, x)), 0') -> false app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(minsort, nil) -> nil app(minsort, app(app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) app(app(min, x), nil) -> x app(app(min, x), app(app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) app(app(del, x), nil) -> nil app(app(del, x), app(app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(le) -> le encArg(0') -> 0' encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0' encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map encode_filter -> filter encode_filter2 -> filter2 Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: 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(eq, 0'), 0') -> true app(app(eq, 0'), app(s, y)) -> false app(app(eq, app(s, x)), 0') -> false app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(minsort, nil) -> nil app(minsort, app(app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) app(app(min, x), nil) -> x app(app(min, x), app(app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) app(app(del, x), nil) -> nil app(app(del, x), app(app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) encArg(le) -> le encArg(0') -> 0' encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0' encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map encode_filter -> filter encode_filter2 -> filter2 Types: app :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app le :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app 0' :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app true :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app s :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app false :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app eq :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app if :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app minsort :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app nil :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app cons :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app min :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app del :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app map :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app filter :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app filter2 :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encArg :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app cons_app :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_app :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_le :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_0 :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_true :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_s :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_false :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_eq :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_if :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_minsort :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_nil :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_cons :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_min :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_del :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_map :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_filter :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_filter2 :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app hole_le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app1_3 :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app gen_le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app2_3 :: Nat -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map: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(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(eq, 0'), 0') -> true app(app(eq, 0'), app(s, y)) -> false app(app(eq, app(s, x)), 0') -> false app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(minsort, nil) -> nil app(minsort, app(app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) app(app(min, x), nil) -> x app(app(min, x), app(app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) app(app(del, x), nil) -> nil app(app(del, x), app(app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) encArg(le) -> le encArg(0') -> 0' encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0' encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map encode_filter -> filter encode_filter2 -> filter2 Types: app :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app le :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app 0' :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app true :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app s :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app false :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app eq :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app if :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app minsort :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app nil :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app cons :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app min :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app del :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app map :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app filter :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app filter2 :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encArg :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app cons_app :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_app :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_le :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_0 :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_true :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_s :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_false :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_eq :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_if :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_minsort :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_nil :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_cons :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_min :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_del :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_map :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_filter :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app encode_filter2 :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app hole_le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app1_3 :: le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app gen_le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app2_3 :: Nat -> le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app Generator Equations: gen_le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app2_3(0) <=> le gen_le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map:filter:filter2:cons_app2_3(+(x, 1)) <=> cons_app(le, gen_le:0':true:s:false:eq:if:minsort:nil:cons:min:del:map: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(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(eq, 0), 0) -> true app(app(eq, 0), app(s, y)) -> false app(app(eq, app(s, x)), 0) -> false app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y) app(app(app(if, true), x), y) -> x app(app(app(if, false), x), y) -> y app(minsort, nil) -> nil app(minsort, app(app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) app(app(min, x), nil) -> x app(app(min, x), app(app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) app(app(del, x), nil) -> nil app(app(del, x), app(app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map 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(minsort, nil) -> nil app(c_app(del, x), nil) -> nil app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(c_app(eq, c_app(s, x)), 0) -> false app(c_app(le, c_app(s, x)), 0) -> false app(c_app(eq, 0), 0) -> true app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y) app(c_app(c_app(if, false), x), y) -> y app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) app(c_app(map, f), nil) -> nil app(c_app(filter, f), nil) -> nil app(c_app(min, x), nil) -> x app(c_app(c_app(if, true), x), y) -> x app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) app(c_app(le, 0), y) -> true app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(c_app(eq, 0), c_app(s, y)) -> false app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) The (relative) TRS S consists of the following rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map 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(minsort, nil) -> nil [1] app(c_app(del, x), nil) -> nil [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(c_app(eq, c_app(s, x)), 0) -> false [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(eq, 0), 0) -> true [1] app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(min, x), nil) -> x [1] app(c_app(c_app(if, true), x), y) -> x [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) [1] app(c_app(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(c_app(eq, 0), c_app(s, y)) -> false [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) [1] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(eq) -> eq [0] encArg(if) -> if [0] encArg(minsort) -> minsort [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(min) -> min [0] encArg(del) -> del [0] encArg(map) -> map [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_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_eq -> eq [0] encode_if -> if [0] encode_minsort -> minsort [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_min -> min [0] encode_del -> del [0] encode_map -> map [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(minsort, nil) -> nil [1] app(c_app(del, x), nil) -> nil [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(c_app(eq, c_app(s, x)), 0) -> false [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(eq, 0), 0) -> true [1] app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(min, x), nil) -> x [1] app(c_app(c_app(if, true), x), y) -> x [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) [1] app(c_app(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(c_app(eq, 0), c_app(s, y)) -> false [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) [1] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(eq) -> eq [0] encArg(if) -> if [0] encArg(minsort) -> minsort [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(min) -> min [0] encArg(del) -> del [0] encArg(map) -> map [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_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_eq -> eq [0] encode_if -> if [0] encode_minsort -> minsort [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_min -> min [0] encode_del -> del [0] encode_map -> map [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 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app c_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app 0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encArg :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app cons_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app encode_filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min: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_le encode_0 encode_true encode_s encode_false encode_eq encode_if encode_minsort encode_nil encode_cons encode_min encode_del encode_map 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_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_eq -> null_encode_eq [0] encode_if -> null_encode_if [0] encode_minsort -> null_encode_minsort [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_min -> null_encode_min [0] encode_del -> null_encode_del [0] encode_map -> null_encode_map [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_le, null_encode_0, null_encode_true, null_encode_s, null_encode_false, null_encode_eq, null_encode_if, null_encode_minsort, null_encode_nil, null_encode_cons, null_encode_min, null_encode_del, null_encode_map, 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(minsort, nil) -> nil [1] app(c_app(del, x), nil) -> nil [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(c_app(eq, c_app(s, x)), 0) -> false [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(eq, 0), 0) -> true [1] app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(min, x), nil) -> x [1] app(c_app(c_app(if, true), x), y) -> x [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) [1] app(c_app(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(c_app(eq, 0), c_app(s, y)) -> false [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) [1] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(eq) -> eq [0] encArg(if) -> if [0] encArg(minsort) -> minsort [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(min) -> min [0] encArg(del) -> del [0] encArg(map) -> map [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_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_eq -> eq [0] encode_if -> if [0] encode_minsort -> minsort [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_min -> min [0] encode_del -> del [0] encode_map -> map [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_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_eq -> null_encode_eq [0] encode_if -> null_encode_if [0] encode_minsort -> null_encode_minsort [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_min -> null_encode_min [0] encode_del -> null_encode_del [0] encode_map -> null_encode_map [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 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app c_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app 0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encArg :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app cons_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encArg :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map: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(minsort, nil) -> nil [1] app(c_app(del, x), nil) -> nil [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(c_app(eq, c_app(s, x)), 0) -> false [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(eq, 0), 0) -> true [1] app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(c_app(eq, x), y) [1] app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(null_app, y) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(c_app(filter, f), xs) [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(null_app, xs) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(c_app(eq, x), y)), z), app(c_app(cons, y), app(c_app(del, x), z))) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(c_app(eq, x), y)), z), app(c_app(cons, y), app(null_app, z))) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(c_app(eq, x), y)), z), app(null_app, app(c_app(del, x), z))) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(c_app(eq, x), y)), z), app(null_app, app(null_app, z))) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(null_app, y)), z), app(c_app(cons, y), app(c_app(del, x), z))) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(null_app, y)), z), app(c_app(cons, y), app(null_app, z))) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(null_app, y)), z), app(null_app, app(c_app(del, x), z))) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(null_app, y)), z), app(null_app, app(null_app, z))) [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(min, x), nil) -> x [1] app(c_app(c_app(if, true), x), y) -> x [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(c_app(min, x), y)), app(minsort, app(app(del, app(c_app(min, x), y)), app(c_app(cons, x), y)))) [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(c_app(min, x), y)), app(minsort, app(app(del, app(c_app(min, x), y)), app(null_app, y)))) [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(c_app(min, x), y)), app(minsort, app(app(del, app(null_app, y)), app(c_app(cons, x), y)))) [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(c_app(min, x), y)), app(minsort, app(app(del, app(null_app, y)), app(null_app, y)))) [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(null_app, y)), app(minsort, app(app(del, app(c_app(min, x), y)), app(c_app(cons, x), y)))) [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(null_app, y)), app(minsort, app(app(del, app(c_app(min, x), y)), app(null_app, y)))) [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(null_app, y)), app(minsort, app(app(del, app(null_app, y)), app(c_app(cons, x), y)))) [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(null_app, y)), app(minsort, app(app(del, app(null_app, y)), app(null_app, y)))) [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(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(c_app(cons, x), app(c_app(filter, f), xs)) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(c_app(cons, x), app(null_app, xs)) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(null_app, app(c_app(filter, f), xs)) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(null_app, app(null_app, xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(c_app(eq, 0), c_app(s, y)) -> false [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(c_app(le, x), y)), app(c_app(min, x), z)), app(c_app(min, y), z)) [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(c_app(le, x), y)), app(c_app(min, x), z)), app(null_app, z)) [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(c_app(le, x), y)), app(null_app, z)), app(c_app(min, y), z)) [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(c_app(le, x), y)), app(null_app, z)), app(null_app, z)) [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(null_app, y)), app(c_app(min, x), z)), app(c_app(min, y), z)) [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(null_app, y)), app(c_app(min, x), z)), app(null_app, z)) [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(null_app, y)), app(null_app, z)), app(c_app(min, y), z)) [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(null_app, y)), app(null_app, z)), app(null_app, z)) [1] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(eq) -> eq [0] encArg(if) -> if [0] encArg(minsort) -> minsort [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(min) -> min [0] encArg(del) -> del [0] encArg(map) -> map [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_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_eq -> eq [0] encode_if -> if [0] encode_minsort -> minsort [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_min -> min [0] encode_del -> del [0] encode_map -> map [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_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_eq -> null_encode_eq [0] encode_if -> null_encode_if [0] encode_minsort -> null_encode_minsort [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_min -> null_encode_min [0] encode_del -> null_encode_del [0] encode_map -> null_encode_map [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 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app c_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app 0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encArg :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app cons_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encArg :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map: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: minsort => 11 nil => 12 del => 2 map => 9 cons => 1 eq => 3 s => 13 0 => 0 false => 4 le => 8 true => 14 if => 7 filter2 => 6 filter => 5 min => 10 null_encArg => 0 null_encode_app => 0 null_encode_le => 0 null_encode_0 => 0 null_encode_true => 0 null_encode_s => 0 null_encode_false => 0 null_encode_eq => 0 null_encode_if => 0 null_encode_minsort => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_min => 0 null_encode_del => 0 null_encode_map => 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 :|: x >= 0, z'' = 12, z' = 1 + 10 + x app(z', z'') -{ 1 }-> x :|: z' = 1 + (1 + 7 + 14) + x, z'' = y, x >= 0, y >= 0 app(z', z'') -{ 1 }-> y :|: z' = 1 + (1 + 7 + 4) + x, z'' = y, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(app(6, app(f, x)), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z' = 1 + 5 + f, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), z), app(0, app(0, z))) :|: z' = 1 + 2 + x, z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), z), app(0, app(1 + 2 + x, z))) :|: z' = 1 + 2 + x, z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), z), app(1 + 1 + y, app(0, z))) :|: z' = 1 + 2 + x, z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), z), app(1 + 1 + y, app(1 + 2 + x, z))) :|: z' = 1 + 2 + x, z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), app(0, z)), app(0, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0, z' = 1 + 10 + x app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), app(0, z)), app(1 + 10 + y, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0, z' = 1 + 10 + x app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), app(1 + 10 + x, z)), app(0, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0, z' = 1 + 10 + x app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), app(1 + 10 + x, z)), app(1 + 10 + y, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0, z' = 1 + 10 + x app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 8 + x, y)), app(0, z)), app(0, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0, z' = 1 + 10 + x app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 8 + x, y)), app(0, z)), app(1 + 10 + y, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0, z' = 1 + 10 + x app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 8 + x, y)), app(1 + 10 + x, z)), app(0, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0, z' = 1 + 10 + x app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 8 + x, y)), app(1 + 10 + x, z)), app(1 + 10 + y, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0, z' = 1 + 10 + x app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 3 + x, y)), z), app(0, app(0, z))) :|: z' = 1 + 2 + x, z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 3 + x, y)), z), app(0, app(1 + 2 + x, z))) :|: z' = 1 + 2 + x, z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 3 + x, y)), z), app(1 + 1 + y, app(0, z))) :|: z' = 1 + 2 + x, z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 3 + x, y)), z), app(1 + 1 + y, app(1 + 2 + x, z))) :|: z' = 1 + 2 + x, z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(1, app(f, x)), app(app(9, f), xs)) :|: f >= 0, z' = 1 + 9 + f, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(app(1, app(0, y)), app(11, app(app(2, app(0, y)), app(0, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(0, y)), app(11, app(app(2, app(0, y)), app(1 + 1 + x, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(0, y)), app(11, app(app(2, app(1 + 10 + x, y)), app(0, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(0, y)), app(11, app(app(2, app(1 + 10 + x, y)), app(1 + 1 + x, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(1 + 10 + x, y)), app(11, app(app(2, app(0, y)), app(0, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(1 + 10 + x, y)), app(11, app(app(2, app(0, y)), app(1 + 1 + x, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(1 + 10 + x, y)), app(11, app(app(2, app(1 + 10 + x, y)), app(0, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(1 + 10 + x, y)), app(11, app(app(2, app(1 + 10 + x, y)), app(1 + 1 + x, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(0, xs) :|: f >= 0, xs >= 0, z' = 1 + (1 + (1 + 6 + 4) + f) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(0, y) :|: z' = 1 + 3 + (1 + 13 + x), x >= 0, y >= 0, z'' = 1 + 13 + y app(z', z'') -{ 1 }-> app(0, y) :|: x >= 0, y >= 0, z'' = 1 + 13 + y, z' = 1 + 8 + (1 + 13 + x) app(z', z'') -{ 1 }-> app(0, app(0, xs)) :|: f >= 0, z' = 1 + (1 + (1 + 6 + 14) + f) + x, xs >= 0, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(0, app(1 + 5 + f, xs)) :|: f >= 0, z' = 1 + (1 + (1 + 6 + 14) + f) + x, xs >= 0, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(1 + 8 + x, y) :|: x >= 0, y >= 0, z'' = 1 + 13 + y, z' = 1 + 8 + (1 + 13 + x) app(z', z'') -{ 1 }-> app(1 + 5 + f, xs) :|: f >= 0, xs >= 0, z' = 1 + (1 + (1 + 6 + 4) + f) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(1 + 3 + x, y) :|: z' = 1 + 3 + (1 + 13 + x), x >= 0, y >= 0, z'' = 1 + 13 + y app(z', z'') -{ 1 }-> app(1 + 1 + x, app(0, xs)) :|: f >= 0, z' = 1 + (1 + (1 + 6 + 14) + f) + x, xs >= 0, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(1 + 1 + x, app(1 + 5 + f, xs)) :|: f >= 0, z' = 1 + (1 + (1 + 6 + 14) + f) + x, xs >= 0, x >= 0, z'' = xs app(z', z'') -{ 1 }-> 4 :|: z'' = 0, z' = 1 + 3 + (1 + 13 + x), x >= 0 app(z', z'') -{ 1 }-> 4 :|: z'' = 0, x >= 0, z' = 1 + 8 + (1 + 13 + x) app(z', z'') -{ 1 }-> 4 :|: y >= 0, z'' = 1 + 13 + y, z' = 1 + 3 + 0 app(z', z'') -{ 1 }-> 14 :|: z'' = 0, z' = 1 + 3 + 0 app(z', z'') -{ 1 }-> 14 :|: z' = 1 + 8 + 0, z'' = y, y >= 0 app(z', z'') -{ 1 }-> 12 :|: z' = 11, z'' = 12 app(z', z'') -{ 1 }-> 12 :|: z' = 1 + 2 + x, x >= 0, z'' = 12 app(z', z'') -{ 1 }-> 12 :|: f >= 0, z' = 1 + 9 + f, z'' = 12 app(z', z'') -{ 1 }-> 12 :|: f >= 0, z' = 1 + 5 + f, z'' = 12 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 }-> 14 :|: z' = 14 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_del -{ 0 }-> 2 :|: encode_del -{ 0 }-> 0 :|: encode_eq -{ 0 }-> 3 :|: encode_eq -{ 0 }-> 0 :|: encode_false -{ 0 }-> 4 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 5 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 6 :|: encode_filter2 -{ 0 }-> 0 :|: encode_if -{ 0 }-> 7 :|: encode_if -{ 0 }-> 0 :|: encode_le -{ 0 }-> 8 :|: encode_le -{ 0 }-> 0 :|: encode_map -{ 0 }-> 9 :|: encode_map -{ 0 }-> 0 :|: encode_min -{ 0 }-> 10 :|: encode_min -{ 0 }-> 0 :|: encode_minsort -{ 0 }-> 11 :|: encode_minsort -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 12 :|: encode_nil -{ 0 }-> 0 :|: encode_s -{ 0 }-> 13 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 14 :|: 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' - 13 >= 0, z'' >= 0 app(z', z'') -{ 1 }-> app(app(app(app(6, app(z' - 6, x)), z' - 6), x), xs) :|: z' - 6 >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), z), app(0, app(0, z))) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 3 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), z), app(0, app(1 + 2 + (z' - 3), z))) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 3 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), z), app(1 + 1 + y, app(0, z))) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 3 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), z), app(1 + 1 + y, app(1 + 2 + (z' - 3), z))) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 3 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), app(0, z)), app(0, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 11 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), app(0, z)), app(1 + 10 + y, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 11 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), app(1 + 10 + (z' - 11), z)), app(0, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 11 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(0, y)), app(1 + 10 + (z' - 11), z)), app(1 + 10 + y, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 11 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 8 + (z' - 11), y)), app(0, z)), app(0, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 11 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 8 + (z' - 11), y)), app(0, z)), app(1 + 10 + y, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 11 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 8 + (z' - 11), y)), app(1 + 10 + (z' - 11), z)), app(0, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 11 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 8 + (z' - 11), y)), app(1 + 10 + (z' - 11), z)), app(1 + 10 + y, z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 11 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 3 + (z' - 3), y)), z), app(0, app(0, z))) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 3 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 3 + (z' - 3), y)), z), app(0, app(1 + 2 + (z' - 3), z))) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 3 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 3 + (z' - 3), y)), z), app(1 + 1 + y, app(0, z))) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 3 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(7, app(1 + 3 + (z' - 3), y)), z), app(1 + 1 + y, app(1 + 2 + (z' - 3), z))) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, z' - 3 >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(1, app(0, y)), app(11, app(app(2, app(0, y)), app(0, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(0, y)), app(11, app(app(2, app(0, y)), app(1 + 1 + x, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(0, y)), app(11, app(app(2, app(1 + 10 + x, y)), app(0, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(0, y)), app(11, app(app(2, app(1 + 10 + x, y)), app(1 + 1 + x, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(z' - 10, x)), app(app(9, z' - 10), xs)) :|: z' - 10 >= 0, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(app(1, app(1 + 10 + x, y)), app(11, app(app(2, app(0, y)), app(0, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(1 + 10 + x, y)), app(11, app(app(2, app(0, y)), app(1 + 1 + x, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(1 + 10 + x, y)), app(11, app(app(2, app(1 + 10 + x, y)), app(0, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(app(1, app(1 + 10 + x, y)), app(11, app(app(2, app(1 + 10 + x, y)), app(1 + 1 + x, y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> app(0, z'') :|: f >= 0, z'' >= 0, z' = 1 + (1 + (1 + 6 + 4) + f) + x, x >= 0 app(z', z'') -{ 1 }-> app(0, app(0, z'')) :|: f >= 0, z' = 1 + (1 + (1 + 6 + 14) + f) + x, z'' >= 0, x >= 0 app(z', z'') -{ 1 }-> app(0, app(1 + 5 + f, z'')) :|: f >= 0, z' = 1 + (1 + (1 + 6 + 14) + f) + x, z'' >= 0, x >= 0 app(z', z'') -{ 1 }-> app(0, z'' - 14) :|: z' - 18 >= 0, z'' - 14 >= 0 app(z', z'') -{ 1 }-> app(0, z'' - 14) :|: z' - 23 >= 0, z'' - 14 >= 0 app(z', z'') -{ 1 }-> app(1 + 8 + (z' - 23), z'' - 14) :|: z' - 23 >= 0, z'' - 14 >= 0 app(z', z'') -{ 1 }-> app(1 + 5 + f, z'') :|: f >= 0, z'' >= 0, z' = 1 + (1 + (1 + 6 + 4) + f) + x, x >= 0 app(z', z'') -{ 1 }-> app(1 + 3 + (z' - 18), z'' - 14) :|: z' - 18 >= 0, z'' - 14 >= 0 app(z', z'') -{ 1 }-> app(1 + 1 + x, app(0, z'')) :|: f >= 0, z' = 1 + (1 + (1 + 6 + 14) + f) + x, z'' >= 0, x >= 0 app(z', z'') -{ 1 }-> app(1 + 1 + x, app(1 + 5 + f, z'')) :|: f >= 0, z' = 1 + (1 + (1 + 6 + 14) + f) + x, z'' >= 0, x >= 0 app(z', z'') -{ 1 }-> 4 :|: z'' = 0, z' - 18 >= 0 app(z', z'') -{ 1 }-> 4 :|: z'' = 0, z' - 23 >= 0 app(z', z'') -{ 1 }-> 4 :|: z'' - 14 >= 0, z' = 1 + 3 + 0 app(z', z'') -{ 1 }-> 14 :|: z'' = 0, z' = 1 + 3 + 0 app(z', z'') -{ 1 }-> 14 :|: z' = 1 + 8 + 0, z'' >= 0 app(z', z'') -{ 1 }-> 12 :|: z' = 11, z'' = 12 app(z', z'') -{ 1 }-> 12 :|: z' - 3 >= 0, z'' = 12 app(z', z'') -{ 1 }-> 12 :|: z' - 10 >= 0, z'' = 12 app(z', z'') -{ 1 }-> 12 :|: z' - 6 >= 0, z'' = 12 app(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0 app(z', z'') -{ 1 }-> z' - 23 :|: z' - 23 >= 0, z'' >= 0 app(z', z'') -{ 1 }-> z' - 11 :|: z' - 11 >= 0, z'' = 12 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 }-> 14 :|: z' = 14 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_del -{ 0 }-> 2 :|: encode_del -{ 0 }-> 0 :|: encode_eq -{ 0 }-> 3 :|: encode_eq -{ 0 }-> 0 :|: encode_false -{ 0 }-> 4 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 5 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 6 :|: encode_filter2 -{ 0 }-> 0 :|: encode_if -{ 0 }-> 7 :|: encode_if -{ 0 }-> 0 :|: encode_le -{ 0 }-> 8 :|: encode_le -{ 0 }-> 0 :|: encode_map -{ 0 }-> 9 :|: encode_map -{ 0 }-> 0 :|: encode_min -{ 0 }-> 10 :|: encode_min -{ 0 }-> 0 :|: encode_minsort -{ 0 }-> 11 :|: encode_minsort -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 12 :|: encode_nil -{ 0 }-> 0 :|: encode_s -{ 0 }-> 13 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 14 :|: 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_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_eq -> null_encode_eq [0] encode_if -> null_encode_if [0] encode_minsort -> null_encode_minsort [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_min -> null_encode_min [0] encode_del -> null_encode_del [0] encode_map -> null_encode_map [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_le, null_encode_0, null_encode_true, null_encode_s, null_encode_false, null_encode_eq, null_encode_if, null_encode_minsort, null_encode_nil, null_encode_cons, null_encode_min, null_encode_del, null_encode_map, 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(minsort, nil) -> nil [1] app(c_app(del, x), nil) -> nil [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(c_app(eq, c_app(s, x)), 0) -> false [1] app(c_app(le, c_app(s, x)), 0) -> false [1] app(c_app(eq, 0), 0) -> true [1] app(c_app(eq, c_app(s, x)), c_app(s, y)) -> app(app(eq, x), y) [1] app(c_app(c_app(if, false), x), y) -> y [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(del, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(eq, x), y)), z), app(app(cons, y), app(app(del, x), z))) [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(min, x), nil) -> x [1] app(c_app(c_app(if, true), x), y) -> x [1] app(minsort, c_app(c_app(cons, x), y)) -> app(app(cons, app(app(min, x), y)), app(minsort, app(app(del, app(app(min, x), y)), app(app(cons, x), y)))) [1] app(c_app(le, c_app(s, x)), c_app(s, y)) -> app(app(le, x), y) [1] app(c_app(le, 0), y) -> true [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(c_app(eq, 0), c_app(s, y)) -> false [1] app(c_app(min, x), c_app(c_app(cons, y), z)) -> app(app(app(if, app(app(le, x), y)), app(app(min, x), z)), app(app(min, y), z)) [1] encArg(le) -> le [0] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s) -> s [0] encArg(false) -> false [0] encArg(eq) -> eq [0] encArg(if) -> if [0] encArg(minsort) -> minsort [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(min) -> min [0] encArg(del) -> del [0] encArg(map) -> map [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_le -> le [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s -> s [0] encode_false -> false [0] encode_eq -> eq [0] encode_if -> if [0] encode_minsort -> minsort [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_min -> min [0] encode_del -> del [0] encode_map -> map [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_le -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s -> null_encode_s [0] encode_false -> null_encode_false [0] encode_eq -> null_encode_eq [0] encode_if -> null_encode_if [0] encode_minsort -> null_encode_minsort [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_min -> null_encode_min [0] encode_del -> null_encode_del [0] encode_map -> null_encode_map [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 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app c_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app 0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encArg :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app cons_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app -> minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app encode_filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encArg :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_le :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_0 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_true :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_s :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_false :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_eq :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_if :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_minsort :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_nil :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_cons :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_min :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_del :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_map :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_filter :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_encode_filter2 :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map:null_encode_filter:null_encode_filter2:null_app null_app :: minsort:nil:del:c_app:map:cons:eq:s:0:false:le:true:if:filter2:filter:min:cons_app:null_encArg:null_encode_app:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_eq:null_encode_if:null_encode_minsort:null_encode_nil:null_encode_cons:null_encode_min:null_encode_del:null_encode_map: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: minsort => 11 nil => 12 del => 2 map => 9 cons => 1 eq => 3 s => 13 0 => 0 false => 4 le => 8 true => 14 if => 7 filter2 => 6 filter => 5 min => 10 null_encArg => 0 null_encode_app => 0 null_encode_le => 0 null_encode_0 => 0 null_encode_true => 0 null_encode_s => 0 null_encode_false => 0 null_encode_eq => 0 null_encode_if => 0 null_encode_minsort => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_min => 0 null_encode_del => 0 null_encode_map => 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 :|: x >= 0, z'' = 12, z' = 1 + 10 + x app(z', z'') -{ 1 }-> x :|: z' = 1 + (1 + 7 + 14) + x, z'' = y, x >= 0, y >= 0 app(z', z'') -{ 1 }-> y :|: z' = 1 + (1 + 7 + 4) + x, z'' = y, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(app(app(6, app(f, x)), f), x), xs) :|: f >= 0, xs >= 0, x >= 0, z' = 1 + 5 + f, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(app(app(7, app(app(8, x), y)), app(app(10, x), z)), app(app(10, y), z)) :|: z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0, z' = 1 + 10 + x app(z', z'') -{ 1 }-> app(app(app(7, app(app(3, x), y)), z), app(app(1, y), app(app(2, x), z))) :|: z' = 1 + 2 + x, z >= 0, z'' = 1 + (1 + 1 + y) + z, x >= 0, y >= 0 app(z', z'') -{ 1 }-> app(app(8, x), y) :|: x >= 0, y >= 0, z'' = 1 + 13 + y, z' = 1 + 8 + (1 + 13 + x) app(z', z'') -{ 1 }-> app(app(5, f), xs) :|: f >= 0, xs >= 0, z' = 1 + (1 + (1 + 6 + 4) + f) + x, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(app(3, x), y) :|: z' = 1 + 3 + (1 + 13 + x), x >= 0, y >= 0, z'' = 1 + 13 + y app(z', z'') -{ 1 }-> app(app(1, x), app(app(5, f), xs)) :|: f >= 0, z' = 1 + (1 + (1 + 6 + 14) + f) + x, xs >= 0, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(app(1, app(f, x)), app(app(9, f), xs)) :|: f >= 0, z' = 1 + 9 + f, xs >= 0, x >= 0, z'' = 1 + (1 + 1 + x) + xs app(z', z'') -{ 1 }-> app(app(1, app(app(10, x), y)), app(11, app(app(2, app(app(10, x), y)), app(app(1, x), y)))) :|: z' = 11, x >= 0, y >= 0, z'' = 1 + (1 + 1 + x) + y app(z', z'') -{ 1 }-> 4 :|: z'' = 0, z' = 1 + 3 + (1 + 13 + x), x >= 0 app(z', z'') -{ 1 }-> 4 :|: z'' = 0, x >= 0, z' = 1 + 8 + (1 + 13 + x) app(z', z'') -{ 1 }-> 4 :|: y >= 0, z'' = 1 + 13 + y, z' = 1 + 3 + 0 app(z', z'') -{ 1 }-> 14 :|: z'' = 0, z' = 1 + 3 + 0 app(z', z'') -{ 1 }-> 14 :|: z' = 1 + 8 + 0, z'' = y, y >= 0 app(z', z'') -{ 1 }-> 12 :|: z' = 11, z'' = 12 app(z', z'') -{ 1 }-> 12 :|: z' = 1 + 2 + x, x >= 0, z'' = 12 app(z', z'') -{ 1 }-> 12 :|: f >= 0, z' = 1 + 9 + f, z'' = 12 app(z', z'') -{ 1 }-> 12 :|: f >= 0, z' = 1 + 5 + f, z'' = 12 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 }-> 14 :|: z' = 14 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_del -{ 0 }-> 2 :|: encode_del -{ 0 }-> 0 :|: encode_eq -{ 0 }-> 3 :|: encode_eq -{ 0 }-> 0 :|: encode_false -{ 0 }-> 4 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 5 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 6 :|: encode_filter2 -{ 0 }-> 0 :|: encode_if -{ 0 }-> 7 :|: encode_if -{ 0 }-> 0 :|: encode_le -{ 0 }-> 8 :|: encode_le -{ 0 }-> 0 :|: encode_map -{ 0 }-> 9 :|: encode_map -{ 0 }-> 0 :|: encode_min -{ 0 }-> 10 :|: encode_min -{ 0 }-> 0 :|: encode_minsort -{ 0 }-> 11 :|: encode_minsort -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 12 :|: encode_nil -{ 0 }-> 0 :|: encode_s -{ 0 }-> 13 :|: encode_s -{ 0 }-> 0 :|: encode_true -{ 0 }-> 14 :|: 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(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map encode_filter -> filter encode_filter2 -> filter2 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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le) -> c ENCARG(0) -> c1 ENCARG(true) -> c2 ENCARG(s) -> c3 ENCARG(false) -> c4 ENCARG(eq) -> c5 ENCARG(if) -> c6 ENCARG(minsort) -> c7 ENCARG(nil) -> c8 ENCARG(cons) -> c9 ENCARG(min) -> c10 ENCARG(del) -> c11 ENCARG(map) -> c12 ENCARG(filter) -> c13 ENCARG(filter2) -> c14 ENCARG(cons_app(z0, z1)) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c16(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_LE -> c17 ENCODE_0 -> c18 ENCODE_TRUE -> c19 ENCODE_S -> c20 ENCODE_FALSE -> c21 ENCODE_EQ -> c22 ENCODE_IF -> c23 ENCODE_MINSORT -> c24 ENCODE_NIL -> c25 ENCODE_CONS -> c26 ENCODE_MIN -> c27 ENCODE_DEL -> c28 ENCODE_MAP -> c29 ENCODE_FILTER -> c30 ENCODE_FILTER2 -> c31 APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1), APP(le, z0)) APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1), APP(eq, z0)) APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))), APP(cons, app(app(min, z0), z1)), APP(app(min, z0), z1), APP(min, z0), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(del, app(app(min, z0), z1)), APP(app(min, z0), z1), APP(min, z0), APP(app(cons, z0), z1), APP(cons, z0)) APP(app(min, z0), nil) -> c43 APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), APP(if, app(app(le, z0), z1)), APP(app(le, z0), z1), APP(le, z0), APP(app(min, z0), z2), APP(min, z0), APP(app(min, z1), z2), APP(min, z1)) APP(app(del, z0), nil) -> c45 APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(if, app(app(eq, z0), z1)), z2), APP(if, app(app(eq, z0), z1)), APP(app(eq, z0), z1), APP(eq, z0), APP(app(cons, z1), app(app(del, z0), z2)), APP(cons, z1), APP(app(del, z0), z2), APP(del, z0)) APP(app(map, z0), nil) -> c47 APP(app(map, z0), app(app(cons, z1), z2)) -> c48(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) -> c49 APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(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) -> c51(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) -> c52(APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1), APP(le, z0)) APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1), APP(eq, z0)) APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))), APP(cons, app(app(min, z0), z1)), APP(app(min, z0), z1), APP(min, z0), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(del, app(app(min, z0), z1)), APP(app(min, z0), z1), APP(min, z0), APP(app(cons, z0), z1), APP(cons, z0)) APP(app(min, z0), nil) -> c43 APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), APP(if, app(app(le, z0), z1)), APP(app(le, z0), z1), APP(le, z0), APP(app(min, z0), z2), APP(min, z0), APP(app(min, z1), z2), APP(min, z1)) APP(app(del, z0), nil) -> c45 APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(if, app(app(eq, z0), z1)), z2), APP(if, app(app(eq, z0), z1)), APP(app(eq, z0), z1), APP(eq, z0), APP(app(cons, z1), app(app(del, z0), z2)), APP(cons, z1), APP(app(del, z0), z2), APP(del, z0)) APP(app(map, z0), nil) -> c47 APP(app(map, z0), app(app(cons, z1), z2)) -> c48(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) -> c49 APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(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) -> c51(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) -> c52(APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_le, encode_0, encode_true, encode_s, encode_false, encode_eq, encode_if, encode_minsort, encode_nil, encode_cons, encode_min, encode_del, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, ENCODE_LE, ENCODE_0, ENCODE_TRUE, ENCODE_S, ENCODE_FALSE, ENCODE_EQ, ENCODE_IF, ENCODE_MINSORT, ENCODE_NIL, ENCODE_CONS, ENCODE_MIN, ENCODE_DEL, ENCODE_MAP, ENCODE_FILTER, ENCODE_FILTER2, APP_2 Compound Symbols: c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15_3, c16_3, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34_2, c35, c36, c37, c38_2, c39, c40, c41, c42_11, c43, c44_9, c45, c46_9, c47, c48_5, c49, c50_5, c51_4, c52_2 ---------------------------------------- (35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 30 trailing nodes: ENCODE_MINSORT -> c24 ENCARG(nil) -> c8 ENCARG(true) -> c2 ENCODE_MIN -> c27 ENCARG(false) -> c4 ENCODE_FILTER -> c30 ENCODE_FALSE -> c21 ENCARG(if) -> c6 ENCARG(del) -> c11 ENCARG(cons) -> c9 ENCARG(eq) -> c5 ENCARG(0) -> c1 ENCODE_DEL -> c28 ENCODE_MAP -> c29 ENCARG(min) -> c10 ENCODE_LE -> c17 ENCARG(filter2) -> c14 ENCARG(minsort) -> c7 ENCODE_TRUE -> c19 ENCARG(filter) -> c13 ENCODE_EQ -> c22 ENCODE_FILTER2 -> c31 ENCARG(s) -> c3 ENCARG(le) -> c ENCODE_NIL -> c25 ENCODE_CONS -> c26 ENCODE_S -> c20 ENCODE_IF -> c23 ENCARG(map) -> c12 ENCODE_0 -> c18 ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map encode_filter -> filter encode_filter2 -> filter2 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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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)) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c16(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1), APP(le, z0)) APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1), APP(eq, z0)) APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))), APP(cons, app(app(min, z0), z1)), APP(app(min, z0), z1), APP(min, z0), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(del, app(app(min, z0), z1)), APP(app(min, z0), z1), APP(min, z0), APP(app(cons, z0), z1), APP(cons, z0)) APP(app(min, z0), nil) -> c43 APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), APP(if, app(app(le, z0), z1)), APP(app(le, z0), z1), APP(le, z0), APP(app(min, z0), z2), APP(min, z0), APP(app(min, z1), z2), APP(min, z1)) APP(app(del, z0), nil) -> c45 APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(if, app(app(eq, z0), z1)), z2), APP(if, app(app(eq, z0), z1)), APP(app(eq, z0), z1), APP(eq, z0), APP(app(cons, z1), app(app(del, z0), z2)), APP(cons, z1), APP(app(del, z0), z2), APP(del, z0)) APP(app(map, z0), nil) -> c47 APP(app(map, z0), app(app(cons, z1), z2)) -> c48(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) -> c49 APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(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) -> c51(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) -> c52(APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1), APP(le, z0)) APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1), APP(eq, z0)) APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))), APP(cons, app(app(min, z0), z1)), APP(app(min, z0), z1), APP(min, z0), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(del, app(app(min, z0), z1)), APP(app(min, z0), z1), APP(min, z0), APP(app(cons, z0), z1), APP(cons, z0)) APP(app(min, z0), nil) -> c43 APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), APP(if, app(app(le, z0), z1)), APP(app(le, z0), z1), APP(le, z0), APP(app(min, z0), z2), APP(min, z0), APP(app(min, z1), z2), APP(min, z1)) APP(app(del, z0), nil) -> c45 APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(if, app(app(eq, z0), z1)), z2), APP(if, app(app(eq, z0), z1)), APP(app(eq, z0), z1), APP(eq, z0), APP(app(cons, z1), app(app(del, z0), z2)), APP(cons, z1), APP(app(del, z0), z2), APP(del, z0)) APP(app(map, z0), nil) -> c47 APP(app(map, z0), app(app(cons, z1), z2)) -> c48(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) -> c49 APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(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) -> c51(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) -> c52(APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_le, encode_0, encode_true, encode_s, encode_false, encode_eq, encode_if, encode_minsort, encode_nil, encode_cons, encode_min, encode_del, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c15_3, c16_3, c32, c33, c34_2, c35, c36, c37, c38_2, c39, c40, c41, c42_11, c43, c44_9, c45, c46_9, c47, c48_5, c49, c50_5, c51_4, c52_2 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 30 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map encode_filter -> filter encode_filter2 -> filter2 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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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)) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c16(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_le, encode_0, encode_true, encode_s, encode_false, encode_eq, encode_if, encode_minsort, encode_nil, encode_cons, encode_min, encode_del, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c15_3, c16_3, c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c42_4, c44_4, c46_3, c48_2, c50_2, c51_1, c52_1 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map encode_filter -> filter encode_filter2 -> filter2 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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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)) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_le, encode_0, encode_true, encode_s, encode_false, encode_eq, encode_if, encode_minsort, encode_nil, encode_cons, encode_min, encode_del, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c15_3, c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c42_4, c44_4, c46_3, c48_2, c50_2, c51_1, c52_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(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map 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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map encode_filter -> filter encode_filter2 -> filter2 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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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)) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_le, encode_0, encode_true, encode_s, encode_false, encode_eq, encode_if, encode_minsort, encode_nil, encode_cons, encode_min, encode_del, encode_map, encode_filter, encode_filter2 Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c15_3, c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c42_4, c44_4, c46_3, c48_2, c50_2, c51_1, c52_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_le -> le encode_0 -> 0 encode_true -> true encode_s -> s encode_false -> false encode_eq -> eq encode_if -> if encode_minsort -> minsort encode_nil -> nil encode_cons -> cons encode_min -> min encode_del -> del encode_map -> map encode_filter -> filter encode_filter2 -> filter2 ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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)) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(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: c15_3, c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c42_4, c44_4, c46_3, c48_2, c50_2, c51_1, c52_1, c_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c15(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0), ENCARG(le)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0), ENCARG(eq)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0), ENCARG(if)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0), ENCARG(minsort)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0), ENCARG(min)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0), ENCARG(del)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(le, x1)) -> c15(APP(le, encArg(x1)), ENCARG(le), ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(APP(eq, encArg(x1)), ENCARG(eq), ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(APP(if, encArg(x1)), ENCARG(if), ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(minsort), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(APP(min, encArg(x1)), ENCARG(min), ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(APP(del, encArg(x1)), ENCARG(del), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0), ENCARG(le)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0), ENCARG(s)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0), ENCARG(eq)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0), ENCARG(if)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0), ENCARG(minsort)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0), ENCARG(min)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0), ENCARG(del)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(le, x1)) -> c15(APP(le, encArg(x1)), ENCARG(le), ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(APP(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(APP(s, encArg(x1)), ENCARG(s), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(APP(eq, encArg(x1)), ENCARG(eq), ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(APP(if, encArg(x1)), ENCARG(if), ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(minsort), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(APP(min, encArg(x1)), ENCARG(min), ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(APP(del, encArg(x1)), ENCARG(del), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c42_4, c44_4, c46_3, c48_2, c50_2, c51_1, c52_1, c_1, c15_3 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 44 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c42_4, c44_4, c46_3, c48_2, c50_2, c51_1, c52_1, c_1, c15_3, c15_2, c15_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(minsort, app(app(cons, z0), z1)) -> c42(APP(app(min, z0), z1), APP(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))), APP(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)), APP(app(min, z0), z1)) by APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c44_4, c46_3, c48_2, c50_2, c51_1, c52_1, c_1, c15_3, c15_2, c15_1, c42_4 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(min, z0), app(app(cons, z1), z2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)), APP(app(le, z0), z1), APP(app(min, z0), z2), APP(app(min, z1), z2)) by APP(app(min, x0), app(app(cons, z0), nil)) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0), APP(app(le, x0), z0), APP(app(min, x0), nil), APP(app(min, z0), nil)) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), nil)) -> c44(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil)), APP(app(le, z0), x1), APP(app(min, z0), nil), APP(app(min, x1), nil)) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), nil)) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0), APP(app(le, x0), z0), APP(app(min, x0), nil), APP(app(min, z0), nil)) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), nil)) -> c44(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil)), APP(app(le, z0), x1), APP(app(min, z0), nil), APP(app(min, x1), nil)) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), nil)) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0), APP(app(le, x0), z0), APP(app(min, x0), nil), APP(app(min, z0), nil)) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), nil)) -> c44(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil)), APP(app(le, z0), x1), APP(app(min, z0), nil), APP(app(min, x1), nil)) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c46_3, c48_2, c50_2, c51_1, c52_1, c_1, c15_3, c15_2, c15_1, c42_4, c44_4 ---------------------------------------- (53) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c46_3, c48_2, c50_2, c51_1, c52_1, c_1, c15_3, c15_2, c15_1, c42_4, c44_4, c1_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(del, z0), app(app(cons, z1), z2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))), APP(app(eq, z0), z1), APP(app(del, z0), z2)) by APP(app(del, z0), app(app(cons, x1), nil)) -> c46(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil)), APP(app(eq, z0), x1), APP(app(del, z0), nil)) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c46(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil)), APP(app(eq, z0), x1), APP(app(del, z0), nil)) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c46(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil)), APP(app(eq, z0), x1), APP(app(del, z0), nil)) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c50_2, c51_1, c52_1, c_1, c15_3, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3 ---------------------------------------- (57) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c50_2, c51_1, c52_1, c_1, c15_3, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c50(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) by APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, minsort), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, nil), minsort), nil), x2), APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))))), minsort), app(app(cons, z0), z1)), x2), APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, nil), app(del, z0)), nil), x2), APP(app(del, z0), nil)) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(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)) -> c50(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)) -> c50(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)) -> c50(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)) -> c50(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)) -> c50(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)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, minsort), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, nil), minsort), nil), x2), APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))))), minsort), app(app(cons, z0), z1)), x2), APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, nil), app(del, z0)), nil), x2), APP(app(del, z0), nil)) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(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)) -> c50(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)) -> c50(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)) -> c50(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)) -> c50(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)) -> c50(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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, minsort), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, nil), minsort), nil), x2), APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1))))), minsort), app(app(cons, z0), z1)), x2), APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, nil), app(del, z0)), nil), x2), APP(app(del, z0), nil)) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(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)) -> c50(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)) -> c50(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)) -> c50(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)) -> c50(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)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c_1, c15_3, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c_1, c15_3, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(le, x1) -> c(APP(le, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(s, x1) -> c(APP(s, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(eq, x1) -> c(APP(eq, encArg(x1))) ENCODE_APP(if, x1) -> c(APP(if, encArg(x1))) ENCODE_APP(minsort, x1) -> c(APP(minsort, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(min, x1) -> c(APP(min, encArg(x1))) ENCODE_APP(del, x1) -> c(APP(del, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, 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))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(le, x1) -> c(APP(le, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(s, x1) -> c(APP(s, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(eq, x1) -> c(APP(eq, encArg(x1))) ENCODE_APP(if, x1) -> c(APP(if, encArg(x1))) ENCODE_APP(minsort, x1) -> c(APP(minsort, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(min, x1) -> c(APP(min, encArg(x1))) ENCODE_APP(del, x1) -> c(APP(del, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_3, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ENCODE_APP(del, x1) -> c(APP(del, encArg(x1))) ENCODE_APP(eq, x1) -> c(APP(eq, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(min, x1) -> c(APP(min, encArg(x1))) ENCODE_APP(if, x1) -> c(APP(if, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(s, x1) -> c(APP(s, encArg(x1))) ENCODE_APP(le, x1) -> c(APP(le, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(0, x1) -> c(APP(0, encArg(x1))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_3, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c15(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by ENCARG(cons_app(x0, cons_app(x1, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(APP(le, app(encArg(x1), encArg(x2))), ENCARG(le), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(APP(eq, app(encArg(x1), encArg(x2))), ENCARG(eq), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(APP(if, app(encArg(x1), encArg(x2))), ENCARG(if), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(minsort), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(APP(min, app(encArg(x1), encArg(x2))), ENCARG(min), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(APP(del, app(encArg(x1), encArg(x2))), ENCARG(del), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(APP(le, app(encArg(x1), encArg(x2))), ENCARG(le), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(APP(0, app(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(APP(s, app(encArg(x1), encArg(x2))), ENCARG(s), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(APP(eq, app(encArg(x1), encArg(x2))), ENCARG(eq), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(APP(if, app(encArg(x1), encArg(x2))), ENCARG(if), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(minsort), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(APP(min, app(encArg(x1), encArg(x2))), ENCARG(min), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(APP(del, app(encArg(x1), encArg(x2))), ENCARG(del), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(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))) -> c15(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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_3, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 29 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_3, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c15(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by ENCARG(cons_app(cons_app(x0, x1), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1)), ENCARG(le)) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)), ENCARG(eq)) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1)), ENCARG(if)) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1)), ENCARG(minsort)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1)), ENCARG(min)) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1)), ENCARG(del)) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(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))) -> c15(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, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(APP(app(if, encArg(x1)), encArg(x2)), ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(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)) -> c15(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, x1), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1)), ENCARG(le)) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1)), ENCARG(0)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1)), ENCARG(s)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1)), ENCARG(eq)) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1)), ENCARG(if)) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1)), ENCARG(minsort)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1)), ENCARG(min)) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1)), ENCARG(del)) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2)) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(APP(app(0, encArg(x1)), encArg(x2)), ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(APP(app(s, encArg(x1)), encArg(x2)), ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(APP(app(if, encArg(x1)), encArg(x2)), ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(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)) -> c15(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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 23 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, le)) -> c15(APP(encArg(x0), le), ENCARG(x0)) by ENCARG(cons_app(le, le)) -> c15(APP(le, le), ENCARG(le)) ENCARG(cons_app(0, le)) -> c15(APP(0, le), ENCARG(0)) ENCARG(cons_app(true, le)) -> c15(APP(true, le), ENCARG(true)) ENCARG(cons_app(s, le)) -> c15(APP(s, le), ENCARG(s)) ENCARG(cons_app(false, le)) -> c15(APP(false, le), ENCARG(false)) ENCARG(cons_app(eq, le)) -> c15(APP(eq, le), ENCARG(eq)) ENCARG(cons_app(if, le)) -> c15(APP(if, le), ENCARG(if)) ENCARG(cons_app(minsort, le)) -> c15(APP(minsort, le), ENCARG(minsort)) ENCARG(cons_app(nil, le)) -> c15(APP(nil, le), ENCARG(nil)) ENCARG(cons_app(cons, le)) -> c15(APP(cons, le), ENCARG(cons)) ENCARG(cons_app(min, le)) -> c15(APP(min, le), ENCARG(min)) ENCARG(cons_app(del, le)) -> c15(APP(del, le), ENCARG(del)) ENCARG(cons_app(map, le)) -> c15(APP(map, le), ENCARG(map)) ENCARG(cons_app(filter, le)) -> c15(APP(filter, le), ENCARG(filter)) ENCARG(cons_app(filter2, le)) -> c15(APP(filter2, le), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), le)) -> c15(APP(app(encArg(z0), encArg(z1)), le), ENCARG(cons_app(z0, z1))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(le, le)) -> c15(APP(le, le), ENCARG(le)) ENCARG(cons_app(0, le)) -> c15(APP(0, le), ENCARG(0)) ENCARG(cons_app(true, le)) -> c15(APP(true, le), ENCARG(true)) ENCARG(cons_app(s, le)) -> c15(APP(s, le), ENCARG(s)) ENCARG(cons_app(false, le)) -> c15(APP(false, le), ENCARG(false)) ENCARG(cons_app(eq, le)) -> c15(APP(eq, le), ENCARG(eq)) ENCARG(cons_app(if, le)) -> c15(APP(if, le), ENCARG(if)) ENCARG(cons_app(minsort, le)) -> c15(APP(minsort, le), ENCARG(minsort)) ENCARG(cons_app(nil, le)) -> c15(APP(nil, le), ENCARG(nil)) ENCARG(cons_app(cons, le)) -> c15(APP(cons, le), ENCARG(cons)) ENCARG(cons_app(min, le)) -> c15(APP(min, le), ENCARG(min)) ENCARG(cons_app(del, le)) -> c15(APP(del, le), ENCARG(del)) ENCARG(cons_app(map, le)) -> c15(APP(map, le), ENCARG(map)) ENCARG(cons_app(filter, le)) -> c15(APP(filter, le), ENCARG(filter)) ENCARG(cons_app(filter2, le)) -> c15(APP(filter2, le), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: ENCARG(cons_app(0, le)) -> c15(APP(0, le), ENCARG(0)) ENCARG(cons_app(minsort, le)) -> c15(APP(minsort, le), ENCARG(minsort)) ENCARG(cons_app(s, le)) -> c15(APP(s, le), ENCARG(s)) ENCARG(cons_app(le, le)) -> c15(APP(le, le), ENCARG(le)) ENCARG(cons_app(filter2, le)) -> c15(APP(filter2, le), ENCARG(filter2)) ENCARG(cons_app(del, le)) -> c15(APP(del, le), ENCARG(del)) ENCARG(cons_app(map, le)) -> c15(APP(map, le), ENCARG(map)) ENCARG(cons_app(false, le)) -> c15(APP(false, le), ENCARG(false)) ENCARG(cons_app(true, le)) -> c15(APP(true, le), ENCARG(true)) ENCARG(cons_app(nil, le)) -> c15(APP(nil, le), ENCARG(nil)) ENCARG(cons_app(if, le)) -> c15(APP(if, le), ENCARG(if)) ENCARG(cons_app(eq, le)) -> c15(APP(eq, le), ENCARG(eq)) ENCARG(cons_app(filter, le)) -> c15(APP(filter, le), ENCARG(filter)) ENCARG(cons_app(min, le)) -> c15(APP(min, le), ENCARG(min)) ENCARG(cons_app(cons, le)) -> c15(APP(cons, le), ENCARG(cons)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, 0)) -> c15(APP(encArg(x0), 0), ENCARG(x0)) by ENCARG(cons_app(le, 0)) -> c15(APP(le, 0), ENCARG(le)) ENCARG(cons_app(0, 0)) -> c15(APP(0, 0), ENCARG(0)) ENCARG(cons_app(true, 0)) -> c15(APP(true, 0), ENCARG(true)) ENCARG(cons_app(s, 0)) -> c15(APP(s, 0), ENCARG(s)) ENCARG(cons_app(false, 0)) -> c15(APP(false, 0), ENCARG(false)) ENCARG(cons_app(eq, 0)) -> c15(APP(eq, 0), ENCARG(eq)) ENCARG(cons_app(if, 0)) -> c15(APP(if, 0), ENCARG(if)) ENCARG(cons_app(minsort, 0)) -> c15(APP(minsort, 0), ENCARG(minsort)) ENCARG(cons_app(nil, 0)) -> c15(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(cons, 0)) -> c15(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(min, 0)) -> c15(APP(min, 0), ENCARG(min)) ENCARG(cons_app(del, 0)) -> c15(APP(del, 0), ENCARG(del)) ENCARG(cons_app(map, 0)) -> c15(APP(map, 0), ENCARG(map)) ENCARG(cons_app(filter, 0)) -> c15(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(filter2, 0)) -> c15(APP(filter2, 0), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), 0)) -> c15(APP(app(encArg(z0), encArg(z1)), 0), ENCARG(cons_app(z0, z1))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(le, 0)) -> c15(APP(le, 0), ENCARG(le)) ENCARG(cons_app(0, 0)) -> c15(APP(0, 0), ENCARG(0)) ENCARG(cons_app(true, 0)) -> c15(APP(true, 0), ENCARG(true)) ENCARG(cons_app(s, 0)) -> c15(APP(s, 0), ENCARG(s)) ENCARG(cons_app(false, 0)) -> c15(APP(false, 0), ENCARG(false)) ENCARG(cons_app(eq, 0)) -> c15(APP(eq, 0), ENCARG(eq)) ENCARG(cons_app(if, 0)) -> c15(APP(if, 0), ENCARG(if)) ENCARG(cons_app(minsort, 0)) -> c15(APP(minsort, 0), ENCARG(minsort)) ENCARG(cons_app(nil, 0)) -> c15(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(cons, 0)) -> c15(APP(cons, 0), ENCARG(cons)) ENCARG(cons_app(min, 0)) -> c15(APP(min, 0), ENCARG(min)) ENCARG(cons_app(del, 0)) -> c15(APP(del, 0), ENCARG(del)) ENCARG(cons_app(map, 0)) -> c15(APP(map, 0), ENCARG(map)) ENCARG(cons_app(filter, 0)) -> c15(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(filter2, 0)) -> c15(APP(filter2, 0), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: ENCARG(cons_app(true, 0)) -> c15(APP(true, 0), ENCARG(true)) ENCARG(cons_app(if, 0)) -> c15(APP(if, 0), ENCARG(if)) ENCARG(cons_app(minsort, 0)) -> c15(APP(minsort, 0), ENCARG(minsort)) ENCARG(cons_app(s, 0)) -> c15(APP(s, 0), ENCARG(s)) ENCARG(cons_app(filter, 0)) -> c15(APP(filter, 0), ENCARG(filter)) ENCARG(cons_app(le, 0)) -> c15(APP(le, 0), ENCARG(le)) ENCARG(cons_app(eq, 0)) -> c15(APP(eq, 0), ENCARG(eq)) ENCARG(cons_app(nil, 0)) -> c15(APP(nil, 0), ENCARG(nil)) ENCARG(cons_app(false, 0)) -> c15(APP(false, 0), ENCARG(false)) ENCARG(cons_app(0, 0)) -> c15(APP(0, 0), ENCARG(0)) ENCARG(cons_app(filter2, 0)) -> c15(APP(filter2, 0), ENCARG(filter2)) ENCARG(cons_app(map, 0)) -> c15(APP(map, 0), ENCARG(map)) ENCARG(cons_app(del, 0)) -> c15(APP(del, 0), ENCARG(del)) ENCARG(cons_app(min, 0)) -> c15(APP(min, 0), ENCARG(min)) ENCARG(cons_app(cons, 0)) -> c15(APP(cons, 0), ENCARG(cons)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, true)) -> c15(APP(encArg(x0), true), ENCARG(x0)) by ENCARG(cons_app(le, true)) -> c15(APP(le, true), ENCARG(le)) ENCARG(cons_app(0, true)) -> c15(APP(0, true), ENCARG(0)) ENCARG(cons_app(true, true)) -> c15(APP(true, true), ENCARG(true)) ENCARG(cons_app(s, true)) -> c15(APP(s, true), ENCARG(s)) ENCARG(cons_app(false, true)) -> c15(APP(false, true), ENCARG(false)) ENCARG(cons_app(eq, true)) -> c15(APP(eq, true), ENCARG(eq)) ENCARG(cons_app(if, true)) -> c15(APP(if, true), ENCARG(if)) ENCARG(cons_app(minsort, true)) -> c15(APP(minsort, true), ENCARG(minsort)) ENCARG(cons_app(nil, true)) -> c15(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c15(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(min, true)) -> c15(APP(min, true), ENCARG(min)) ENCARG(cons_app(del, true)) -> c15(APP(del, true), ENCARG(del)) ENCARG(cons_app(map, true)) -> c15(APP(map, true), ENCARG(map)) ENCARG(cons_app(filter, true)) -> c15(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(filter2, true)) -> c15(APP(filter2, true), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), true)) -> c15(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(le, true)) -> c15(APP(le, true), ENCARG(le)) ENCARG(cons_app(0, true)) -> c15(APP(0, true), ENCARG(0)) ENCARG(cons_app(true, true)) -> c15(APP(true, true), ENCARG(true)) ENCARG(cons_app(s, true)) -> c15(APP(s, true), ENCARG(s)) ENCARG(cons_app(false, true)) -> c15(APP(false, true), ENCARG(false)) ENCARG(cons_app(eq, true)) -> c15(APP(eq, true), ENCARG(eq)) ENCARG(cons_app(if, true)) -> c15(APP(if, true), ENCARG(if)) ENCARG(cons_app(minsort, true)) -> c15(APP(minsort, true), ENCARG(minsort)) ENCARG(cons_app(nil, true)) -> c15(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c15(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(min, true)) -> c15(APP(min, true), ENCARG(min)) ENCARG(cons_app(del, true)) -> c15(APP(del, true), ENCARG(del)) ENCARG(cons_app(map, true)) -> c15(APP(map, true), ENCARG(map)) ENCARG(cons_app(filter, true)) -> c15(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(filter2, true)) -> c15(APP(filter2, true), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: ENCARG(cons_app(minsort, true)) -> c15(APP(minsort, true), ENCARG(minsort)) ENCARG(cons_app(s, true)) -> c15(APP(s, true), ENCARG(s)) ENCARG(cons_app(le, true)) -> c15(APP(le, true), ENCARG(le)) ENCARG(cons_app(if, true)) -> c15(APP(if, true), ENCARG(if)) ENCARG(cons_app(eq, true)) -> c15(APP(eq, true), ENCARG(eq)) ENCARG(cons_app(filter, true)) -> c15(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(del, true)) -> c15(APP(del, true), ENCARG(del)) ENCARG(cons_app(min, true)) -> c15(APP(min, true), ENCARG(min)) ENCARG(cons_app(cons, true)) -> c15(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(0, true)) -> c15(APP(0, true), ENCARG(0)) ENCARG(cons_app(true, true)) -> c15(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c15(APP(false, true), ENCARG(false)) ENCARG(cons_app(filter2, true)) -> c15(APP(filter2, true), ENCARG(filter2)) ENCARG(cons_app(map, true)) -> c15(APP(map, true), ENCARG(map)) ENCARG(cons_app(nil, true)) -> c15(APP(nil, true), ENCARG(nil)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, s)) -> c15(APP(encArg(x0), s), ENCARG(x0)) by ENCARG(cons_app(le, s)) -> c15(APP(le, s), ENCARG(le)) ENCARG(cons_app(0, s)) -> c15(APP(0, s), ENCARG(0)) ENCARG(cons_app(true, s)) -> c15(APP(true, s), ENCARG(true)) ENCARG(cons_app(s, s)) -> c15(APP(s, s), ENCARG(s)) ENCARG(cons_app(false, s)) -> c15(APP(false, s), ENCARG(false)) ENCARG(cons_app(eq, s)) -> c15(APP(eq, s), ENCARG(eq)) ENCARG(cons_app(if, s)) -> c15(APP(if, s), ENCARG(if)) ENCARG(cons_app(minsort, s)) -> c15(APP(minsort, s), ENCARG(minsort)) ENCARG(cons_app(nil, s)) -> c15(APP(nil, s), ENCARG(nil)) ENCARG(cons_app(cons, s)) -> c15(APP(cons, s), ENCARG(cons)) ENCARG(cons_app(min, s)) -> c15(APP(min, s), ENCARG(min)) ENCARG(cons_app(del, s)) -> c15(APP(del, s), ENCARG(del)) ENCARG(cons_app(map, s)) -> c15(APP(map, s), ENCARG(map)) ENCARG(cons_app(filter, s)) -> c15(APP(filter, s), ENCARG(filter)) ENCARG(cons_app(filter2, s)) -> c15(APP(filter2, s), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), s)) -> c15(APP(app(encArg(z0), encArg(z1)), s), ENCARG(cons_app(z0, z1))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(le, s)) -> c15(APP(le, s), ENCARG(le)) ENCARG(cons_app(0, s)) -> c15(APP(0, s), ENCARG(0)) ENCARG(cons_app(true, s)) -> c15(APP(true, s), ENCARG(true)) ENCARG(cons_app(s, s)) -> c15(APP(s, s), ENCARG(s)) ENCARG(cons_app(false, s)) -> c15(APP(false, s), ENCARG(false)) ENCARG(cons_app(eq, s)) -> c15(APP(eq, s), ENCARG(eq)) ENCARG(cons_app(if, s)) -> c15(APP(if, s), ENCARG(if)) ENCARG(cons_app(minsort, s)) -> c15(APP(minsort, s), ENCARG(minsort)) ENCARG(cons_app(nil, s)) -> c15(APP(nil, s), ENCARG(nil)) ENCARG(cons_app(cons, s)) -> c15(APP(cons, s), ENCARG(cons)) ENCARG(cons_app(min, s)) -> c15(APP(min, s), ENCARG(min)) ENCARG(cons_app(del, s)) -> c15(APP(del, s), ENCARG(del)) ENCARG(cons_app(map, s)) -> c15(APP(map, s), ENCARG(map)) ENCARG(cons_app(filter, s)) -> c15(APP(filter, s), ENCARG(filter)) ENCARG(cons_app(filter2, s)) -> c15(APP(filter2, s), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: ENCARG(cons_app(nil, s)) -> c15(APP(nil, s), ENCARG(nil)) ENCARG(cons_app(le, s)) -> c15(APP(le, s), ENCARG(le)) ENCARG(cons_app(map, s)) -> c15(APP(map, s), ENCARG(map)) ENCARG(cons_app(false, s)) -> c15(APP(false, s), ENCARG(false)) ENCARG(cons_app(filter2, s)) -> c15(APP(filter2, s), ENCARG(filter2)) ENCARG(cons_app(true, s)) -> c15(APP(true, s), ENCARG(true)) ENCARG(cons_app(if, s)) -> c15(APP(if, s), ENCARG(if)) ENCARG(cons_app(del, s)) -> c15(APP(del, s), ENCARG(del)) ENCARG(cons_app(cons, s)) -> c15(APP(cons, s), ENCARG(cons)) ENCARG(cons_app(filter, s)) -> c15(APP(filter, s), ENCARG(filter)) ENCARG(cons_app(0, s)) -> c15(APP(0, s), ENCARG(0)) ENCARG(cons_app(minsort, s)) -> c15(APP(minsort, s), ENCARG(minsort)) ENCARG(cons_app(s, s)) -> c15(APP(s, s), ENCARG(s)) ENCARG(cons_app(min, s)) -> c15(APP(min, s), ENCARG(min)) ENCARG(cons_app(eq, s)) -> c15(APP(eq, s), ENCARG(eq)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, false)) -> c15(APP(encArg(x0), false), ENCARG(x0)) by ENCARG(cons_app(le, false)) -> c15(APP(le, false), ENCARG(le)) ENCARG(cons_app(0, false)) -> c15(APP(0, false), ENCARG(0)) ENCARG(cons_app(true, false)) -> c15(APP(true, false), ENCARG(true)) ENCARG(cons_app(s, false)) -> c15(APP(s, false), ENCARG(s)) ENCARG(cons_app(false, false)) -> c15(APP(false, false), ENCARG(false)) ENCARG(cons_app(eq, false)) -> c15(APP(eq, false), ENCARG(eq)) ENCARG(cons_app(if, false)) -> c15(APP(if, false), ENCARG(if)) ENCARG(cons_app(minsort, false)) -> c15(APP(minsort, false), ENCARG(minsort)) ENCARG(cons_app(nil, false)) -> c15(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c15(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(min, false)) -> c15(APP(min, false), ENCARG(min)) ENCARG(cons_app(del, false)) -> c15(APP(del, false), ENCARG(del)) ENCARG(cons_app(map, false)) -> c15(APP(map, false), ENCARG(map)) ENCARG(cons_app(filter, false)) -> c15(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(filter2, false)) -> c15(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), false)) -> c15(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(le, false)) -> c15(APP(le, false), ENCARG(le)) ENCARG(cons_app(0, false)) -> c15(APP(0, false), ENCARG(0)) ENCARG(cons_app(true, false)) -> c15(APP(true, false), ENCARG(true)) ENCARG(cons_app(s, false)) -> c15(APP(s, false), ENCARG(s)) ENCARG(cons_app(false, false)) -> c15(APP(false, false), ENCARG(false)) ENCARG(cons_app(eq, false)) -> c15(APP(eq, false), ENCARG(eq)) ENCARG(cons_app(if, false)) -> c15(APP(if, false), ENCARG(if)) ENCARG(cons_app(minsort, false)) -> c15(APP(minsort, false), ENCARG(minsort)) ENCARG(cons_app(nil, false)) -> c15(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c15(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(min, false)) -> c15(APP(min, false), ENCARG(min)) ENCARG(cons_app(del, false)) -> c15(APP(del, false), ENCARG(del)) ENCARG(cons_app(map, false)) -> c15(APP(map, false), ENCARG(map)) ENCARG(cons_app(filter, false)) -> c15(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(filter2, false)) -> c15(APP(filter2, false), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: ENCARG(cons_app(true, false)) -> c15(APP(true, false), ENCARG(true)) ENCARG(cons_app(0, false)) -> c15(APP(0, false), ENCARG(0)) ENCARG(cons_app(nil, false)) -> c15(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(minsort, false)) -> c15(APP(minsort, false), ENCARG(minsort)) ENCARG(cons_app(if, false)) -> c15(APP(if, false), ENCARG(if)) ENCARG(cons_app(s, false)) -> c15(APP(s, false), ENCARG(s)) ENCARG(cons_app(le, false)) -> c15(APP(le, false), ENCARG(le)) ENCARG(cons_app(del, false)) -> c15(APP(del, false), ENCARG(del)) ENCARG(cons_app(min, false)) -> c15(APP(min, false), ENCARG(min)) ENCARG(cons_app(filter, false)) -> c15(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(cons, false)) -> c15(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(false, false)) -> c15(APP(false, false), ENCARG(false)) ENCARG(cons_app(map, false)) -> c15(APP(map, false), ENCARG(map)) ENCARG(cons_app(filter2, false)) -> c15(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(eq, false)) -> c15(APP(eq, false), ENCARG(eq)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, eq)) -> c15(APP(encArg(x0), eq), ENCARG(x0)) by ENCARG(cons_app(le, eq)) -> c15(APP(le, eq), ENCARG(le)) ENCARG(cons_app(0, eq)) -> c15(APP(0, eq), ENCARG(0)) ENCARG(cons_app(true, eq)) -> c15(APP(true, eq), ENCARG(true)) ENCARG(cons_app(s, eq)) -> c15(APP(s, eq), ENCARG(s)) ENCARG(cons_app(false, eq)) -> c15(APP(false, eq), ENCARG(false)) ENCARG(cons_app(eq, eq)) -> c15(APP(eq, eq), ENCARG(eq)) ENCARG(cons_app(if, eq)) -> c15(APP(if, eq), ENCARG(if)) ENCARG(cons_app(minsort, eq)) -> c15(APP(minsort, eq), ENCARG(minsort)) ENCARG(cons_app(nil, eq)) -> c15(APP(nil, eq), ENCARG(nil)) ENCARG(cons_app(cons, eq)) -> c15(APP(cons, eq), ENCARG(cons)) ENCARG(cons_app(min, eq)) -> c15(APP(min, eq), ENCARG(min)) ENCARG(cons_app(del, eq)) -> c15(APP(del, eq), ENCARG(del)) ENCARG(cons_app(map, eq)) -> c15(APP(map, eq), ENCARG(map)) ENCARG(cons_app(filter, eq)) -> c15(APP(filter, eq), ENCARG(filter)) ENCARG(cons_app(filter2, eq)) -> c15(APP(filter2, eq), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), eq)) -> c15(APP(app(encArg(z0), encArg(z1)), eq), ENCARG(cons_app(z0, z1))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(le, eq)) -> c15(APP(le, eq), ENCARG(le)) ENCARG(cons_app(0, eq)) -> c15(APP(0, eq), ENCARG(0)) ENCARG(cons_app(true, eq)) -> c15(APP(true, eq), ENCARG(true)) ENCARG(cons_app(s, eq)) -> c15(APP(s, eq), ENCARG(s)) ENCARG(cons_app(false, eq)) -> c15(APP(false, eq), ENCARG(false)) ENCARG(cons_app(eq, eq)) -> c15(APP(eq, eq), ENCARG(eq)) ENCARG(cons_app(if, eq)) -> c15(APP(if, eq), ENCARG(if)) ENCARG(cons_app(minsort, eq)) -> c15(APP(minsort, eq), ENCARG(minsort)) ENCARG(cons_app(nil, eq)) -> c15(APP(nil, eq), ENCARG(nil)) ENCARG(cons_app(cons, eq)) -> c15(APP(cons, eq), ENCARG(cons)) ENCARG(cons_app(min, eq)) -> c15(APP(min, eq), ENCARG(min)) ENCARG(cons_app(del, eq)) -> c15(APP(del, eq), ENCARG(del)) ENCARG(cons_app(map, eq)) -> c15(APP(map, eq), ENCARG(map)) ENCARG(cons_app(filter, eq)) -> c15(APP(filter, eq), ENCARG(filter)) ENCARG(cons_app(filter2, eq)) -> c15(APP(filter2, eq), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: ENCARG(cons_app(if, eq)) -> c15(APP(if, eq), ENCARG(if)) ENCARG(cons_app(filter2, eq)) -> c15(APP(filter2, eq), ENCARG(filter2)) ENCARG(cons_app(cons, eq)) -> c15(APP(cons, eq), ENCARG(cons)) ENCARG(cons_app(false, eq)) -> c15(APP(false, eq), ENCARG(false)) ENCARG(cons_app(true, eq)) -> c15(APP(true, eq), ENCARG(true)) ENCARG(cons_app(map, eq)) -> c15(APP(map, eq), ENCARG(map)) ENCARG(cons_app(del, eq)) -> c15(APP(del, eq), ENCARG(del)) ENCARG(cons_app(le, eq)) -> c15(APP(le, eq), ENCARG(le)) ENCARG(cons_app(filter, eq)) -> c15(APP(filter, eq), ENCARG(filter)) ENCARG(cons_app(nil, eq)) -> c15(APP(nil, eq), ENCARG(nil)) ENCARG(cons_app(min, eq)) -> c15(APP(min, eq), ENCARG(min)) ENCARG(cons_app(minsort, eq)) -> c15(APP(minsort, eq), ENCARG(minsort)) ENCARG(cons_app(s, eq)) -> c15(APP(s, eq), ENCARG(s)) ENCARG(cons_app(eq, eq)) -> c15(APP(eq, eq), ENCARG(eq)) ENCARG(cons_app(0, eq)) -> c15(APP(0, eq), ENCARG(0)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, if)) -> c15(APP(encArg(x0), if), ENCARG(x0)) by ENCARG(cons_app(le, if)) -> c15(APP(le, if), ENCARG(le)) ENCARG(cons_app(0, if)) -> c15(APP(0, if), ENCARG(0)) ENCARG(cons_app(true, if)) -> c15(APP(true, if), ENCARG(true)) ENCARG(cons_app(s, if)) -> c15(APP(s, if), ENCARG(s)) ENCARG(cons_app(false, if)) -> c15(APP(false, if), ENCARG(false)) ENCARG(cons_app(eq, if)) -> c15(APP(eq, if), ENCARG(eq)) ENCARG(cons_app(if, if)) -> c15(APP(if, if), ENCARG(if)) ENCARG(cons_app(minsort, if)) -> c15(APP(minsort, if), ENCARG(minsort)) ENCARG(cons_app(nil, if)) -> c15(APP(nil, if), ENCARG(nil)) ENCARG(cons_app(cons, if)) -> c15(APP(cons, if), ENCARG(cons)) ENCARG(cons_app(min, if)) -> c15(APP(min, if), ENCARG(min)) ENCARG(cons_app(del, if)) -> c15(APP(del, if), ENCARG(del)) ENCARG(cons_app(map, if)) -> c15(APP(map, if), ENCARG(map)) ENCARG(cons_app(filter, if)) -> c15(APP(filter, if), ENCARG(filter)) ENCARG(cons_app(filter2, if)) -> c15(APP(filter2, if), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), if)) -> c15(APP(app(encArg(z0), encArg(z1)), if), ENCARG(cons_app(z0, z1))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(le, if)) -> c15(APP(le, if), ENCARG(le)) ENCARG(cons_app(0, if)) -> c15(APP(0, if), ENCARG(0)) ENCARG(cons_app(true, if)) -> c15(APP(true, if), ENCARG(true)) ENCARG(cons_app(s, if)) -> c15(APP(s, if), ENCARG(s)) ENCARG(cons_app(false, if)) -> c15(APP(false, if), ENCARG(false)) ENCARG(cons_app(eq, if)) -> c15(APP(eq, if), ENCARG(eq)) ENCARG(cons_app(if, if)) -> c15(APP(if, if), ENCARG(if)) ENCARG(cons_app(minsort, if)) -> c15(APP(minsort, if), ENCARG(minsort)) ENCARG(cons_app(nil, if)) -> c15(APP(nil, if), ENCARG(nil)) ENCARG(cons_app(cons, if)) -> c15(APP(cons, if), ENCARG(cons)) ENCARG(cons_app(min, if)) -> c15(APP(min, if), ENCARG(min)) ENCARG(cons_app(del, if)) -> c15(APP(del, if), ENCARG(del)) ENCARG(cons_app(map, if)) -> c15(APP(map, if), ENCARG(map)) ENCARG(cons_app(filter, if)) -> c15(APP(filter, if), ENCARG(filter)) ENCARG(cons_app(filter2, if)) -> c15(APP(filter2, if), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: ENCARG(cons_app(0, if)) -> c15(APP(0, if), ENCARG(0)) ENCARG(cons_app(true, if)) -> c15(APP(true, if), ENCARG(true)) ENCARG(cons_app(nil, if)) -> c15(APP(nil, if), ENCARG(nil)) ENCARG(cons_app(minsort, if)) -> c15(APP(minsort, if), ENCARG(minsort)) ENCARG(cons_app(s, if)) -> c15(APP(s, if), ENCARG(s)) ENCARG(cons_app(cons, if)) -> c15(APP(cons, if), ENCARG(cons)) ENCARG(cons_app(le, if)) -> c15(APP(le, if), ENCARG(le)) ENCARG(cons_app(if, if)) -> c15(APP(if, if), ENCARG(if)) ENCARG(cons_app(filter2, if)) -> c15(APP(filter2, if), ENCARG(filter2)) ENCARG(cons_app(filter, if)) -> c15(APP(filter, if), ENCARG(filter)) ENCARG(cons_app(min, if)) -> c15(APP(min, if), ENCARG(min)) ENCARG(cons_app(map, if)) -> c15(APP(map, if), ENCARG(map)) ENCARG(cons_app(del, if)) -> c15(APP(del, if), ENCARG(del)) ENCARG(cons_app(eq, if)) -> c15(APP(eq, if), ENCARG(eq)) ENCARG(cons_app(false, if)) -> c15(APP(false, if), ENCARG(false)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, minsort)) -> c15(APP(encArg(x0), minsort), ENCARG(x0)) by ENCARG(cons_app(le, minsort)) -> c15(APP(le, minsort), ENCARG(le)) ENCARG(cons_app(0, minsort)) -> c15(APP(0, minsort), ENCARG(0)) ENCARG(cons_app(true, minsort)) -> c15(APP(true, minsort), ENCARG(true)) ENCARG(cons_app(s, minsort)) -> c15(APP(s, minsort), ENCARG(s)) ENCARG(cons_app(false, minsort)) -> c15(APP(false, minsort), ENCARG(false)) ENCARG(cons_app(eq, minsort)) -> c15(APP(eq, minsort), ENCARG(eq)) ENCARG(cons_app(if, minsort)) -> c15(APP(if, minsort), ENCARG(if)) ENCARG(cons_app(minsort, minsort)) -> c15(APP(minsort, minsort), ENCARG(minsort)) ENCARG(cons_app(nil, minsort)) -> c15(APP(nil, minsort), ENCARG(nil)) ENCARG(cons_app(cons, minsort)) -> c15(APP(cons, minsort), ENCARG(cons)) ENCARG(cons_app(min, minsort)) -> c15(APP(min, minsort), ENCARG(min)) ENCARG(cons_app(del, minsort)) -> c15(APP(del, minsort), ENCARG(del)) ENCARG(cons_app(map, minsort)) -> c15(APP(map, minsort), ENCARG(map)) ENCARG(cons_app(filter, minsort)) -> c15(APP(filter, minsort), ENCARG(filter)) ENCARG(cons_app(filter2, minsort)) -> c15(APP(filter2, minsort), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), minsort)) -> c15(APP(app(encArg(z0), encArg(z1)), minsort), ENCARG(cons_app(z0, z1))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(le, minsort)) -> c15(APP(le, minsort), ENCARG(le)) ENCARG(cons_app(0, minsort)) -> c15(APP(0, minsort), ENCARG(0)) ENCARG(cons_app(true, minsort)) -> c15(APP(true, minsort), ENCARG(true)) ENCARG(cons_app(s, minsort)) -> c15(APP(s, minsort), ENCARG(s)) ENCARG(cons_app(false, minsort)) -> c15(APP(false, minsort), ENCARG(false)) ENCARG(cons_app(eq, minsort)) -> c15(APP(eq, minsort), ENCARG(eq)) ENCARG(cons_app(if, minsort)) -> c15(APP(if, minsort), ENCARG(if)) ENCARG(cons_app(minsort, minsort)) -> c15(APP(minsort, minsort), ENCARG(minsort)) ENCARG(cons_app(nil, minsort)) -> c15(APP(nil, minsort), ENCARG(nil)) ENCARG(cons_app(cons, minsort)) -> c15(APP(cons, minsort), ENCARG(cons)) ENCARG(cons_app(min, minsort)) -> c15(APP(min, minsort), ENCARG(min)) ENCARG(cons_app(del, minsort)) -> c15(APP(del, minsort), ENCARG(del)) ENCARG(cons_app(map, minsort)) -> c15(APP(map, minsort), ENCARG(map)) ENCARG(cons_app(filter, minsort)) -> c15(APP(filter, minsort), ENCARG(filter)) ENCARG(cons_app(filter2, minsort)) -> c15(APP(filter2, minsort), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: ENCARG(cons_app(true, minsort)) -> c15(APP(true, minsort), ENCARG(true)) ENCARG(cons_app(filter, minsort)) -> c15(APP(filter, minsort), ENCARG(filter)) ENCARG(cons_app(le, minsort)) -> c15(APP(le, minsort), ENCARG(le)) ENCARG(cons_app(eq, minsort)) -> c15(APP(eq, minsort), ENCARG(eq)) ENCARG(cons_app(map, minsort)) -> c15(APP(map, minsort), ENCARG(map)) ENCARG(cons_app(nil, minsort)) -> c15(APP(nil, minsort), ENCARG(nil)) ENCARG(cons_app(cons, minsort)) -> c15(APP(cons, minsort), ENCARG(cons)) ENCARG(cons_app(min, minsort)) -> c15(APP(min, minsort), ENCARG(min)) ENCARG(cons_app(if, minsort)) -> c15(APP(if, minsort), ENCARG(if)) ENCARG(cons_app(0, minsort)) -> c15(APP(0, minsort), ENCARG(0)) ENCARG(cons_app(filter2, minsort)) -> c15(APP(filter2, minsort), ENCARG(filter2)) ENCARG(cons_app(del, minsort)) -> c15(APP(del, minsort), ENCARG(del)) ENCARG(cons_app(false, minsort)) -> c15(APP(false, minsort), ENCARG(false)) ENCARG(cons_app(minsort, minsort)) -> c15(APP(minsort, minsort), ENCARG(minsort)) ENCARG(cons_app(s, minsort)) -> c15(APP(s, minsort), ENCARG(s)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c15(APP(encArg(x0), nil), ENCARG(x0)) by ENCARG(cons_app(le, nil)) -> c15(APP(le, nil), ENCARG(le)) ENCARG(cons_app(0, nil)) -> c15(APP(0, nil), ENCARG(0)) ENCARG(cons_app(true, nil)) -> c15(APP(true, nil), ENCARG(true)) ENCARG(cons_app(s, nil)) -> c15(APP(s, nil), ENCARG(s)) ENCARG(cons_app(false, nil)) -> c15(APP(false, nil), ENCARG(false)) ENCARG(cons_app(eq, nil)) -> c15(APP(eq, nil), ENCARG(eq)) ENCARG(cons_app(if, nil)) -> c15(APP(if, nil), ENCARG(if)) ENCARG(cons_app(minsort, nil)) -> c15(APP(minsort, nil), ENCARG(minsort)) ENCARG(cons_app(nil, nil)) -> c15(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c15(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(min, nil)) -> c15(APP(min, nil), ENCARG(min)) ENCARG(cons_app(del, nil)) -> c15(APP(del, nil), ENCARG(del)) ENCARG(cons_app(map, nil)) -> c15(APP(map, nil), ENCARG(map)) ENCARG(cons_app(filter, nil)) -> c15(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(filter2, nil)) -> c15(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), nil)) -> c15(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(le, nil)) -> c15(APP(le, nil), ENCARG(le)) ENCARG(cons_app(0, nil)) -> c15(APP(0, nil), ENCARG(0)) ENCARG(cons_app(true, nil)) -> c15(APP(true, nil), ENCARG(true)) ENCARG(cons_app(s, nil)) -> c15(APP(s, nil), ENCARG(s)) ENCARG(cons_app(false, nil)) -> c15(APP(false, nil), ENCARG(false)) ENCARG(cons_app(eq, nil)) -> c15(APP(eq, nil), ENCARG(eq)) ENCARG(cons_app(if, nil)) -> c15(APP(if, nil), ENCARG(if)) ENCARG(cons_app(minsort, nil)) -> c15(APP(minsort, nil), ENCARG(minsort)) ENCARG(cons_app(nil, nil)) -> c15(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c15(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(min, nil)) -> c15(APP(min, nil), ENCARG(min)) ENCARG(cons_app(del, nil)) -> c15(APP(del, nil), ENCARG(del)) ENCARG(cons_app(map, nil)) -> c15(APP(map, nil), ENCARG(map)) ENCARG(cons_app(filter, nil)) -> c15(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(filter2, nil)) -> c15(APP(filter2, nil), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: ENCARG(cons_app(if, nil)) -> c15(APP(if, nil), ENCARG(if)) ENCARG(cons_app(filter2, nil)) -> c15(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(min, nil)) -> c15(APP(min, nil), ENCARG(min)) ENCARG(cons_app(false, nil)) -> c15(APP(false, nil), ENCARG(false)) ENCARG(cons_app(filter, nil)) -> c15(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(cons, nil)) -> c15(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(nil, nil)) -> c15(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(true, nil)) -> c15(APP(true, nil), ENCARG(true)) ENCARG(cons_app(del, nil)) -> c15(APP(del, nil), ENCARG(del)) ENCARG(cons_app(le, nil)) -> c15(APP(le, nil), ENCARG(le)) ENCARG(cons_app(s, nil)) -> c15(APP(s, nil), ENCARG(s)) ENCARG(cons_app(eq, nil)) -> c15(APP(eq, nil), ENCARG(eq)) ENCARG(cons_app(0, nil)) -> c15(APP(0, nil), ENCARG(0)) ENCARG(cons_app(map, nil)) -> c15(APP(map, nil), ENCARG(map)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(minsort, nil)) -> c15(APP(minsort, nil), ENCARG(minsort)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(minsort, nil)) -> c15(APP(minsort, nil)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c15(APP(encArg(x0), cons), ENCARG(x0)) by ENCARG(cons_app(le, cons)) -> c15(APP(le, cons), ENCARG(le)) ENCARG(cons_app(0, cons)) -> c15(APP(0, cons), ENCARG(0)) ENCARG(cons_app(true, cons)) -> c15(APP(true, cons), ENCARG(true)) ENCARG(cons_app(s, cons)) -> c15(APP(s, cons), ENCARG(s)) ENCARG(cons_app(false, cons)) -> c15(APP(false, cons), ENCARG(false)) ENCARG(cons_app(eq, cons)) -> c15(APP(eq, cons), ENCARG(eq)) ENCARG(cons_app(if, cons)) -> c15(APP(if, cons), ENCARG(if)) ENCARG(cons_app(minsort, cons)) -> c15(APP(minsort, cons), ENCARG(minsort)) ENCARG(cons_app(nil, cons)) -> c15(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c15(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(min, cons)) -> c15(APP(min, cons), ENCARG(min)) ENCARG(cons_app(del, cons)) -> c15(APP(del, cons), ENCARG(del)) ENCARG(cons_app(map, cons)) -> c15(APP(map, cons), ENCARG(map)) ENCARG(cons_app(filter, cons)) -> c15(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(filter2, cons)) -> c15(APP(filter2, cons), ENCARG(filter2)) ENCARG(cons_app(cons_app(z0, z1), cons)) -> c15(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(minsort, nil)) -> c15(APP(minsort, nil)) ENCARG(cons_app(le, cons)) -> c15(APP(le, cons), ENCARG(le)) ENCARG(cons_app(0, cons)) -> c15(APP(0, cons), ENCARG(0)) ENCARG(cons_app(true, cons)) -> c15(APP(true, cons), ENCARG(true)) ENCARG(cons_app(s, cons)) -> c15(APP(s, cons), ENCARG(s)) ENCARG(cons_app(false, cons)) -> c15(APP(false, cons), ENCARG(false)) ENCARG(cons_app(eq, cons)) -> c15(APP(eq, cons), ENCARG(eq)) ENCARG(cons_app(if, cons)) -> c15(APP(if, cons), ENCARG(if)) ENCARG(cons_app(minsort, cons)) -> c15(APP(minsort, cons), ENCARG(minsort)) ENCARG(cons_app(nil, cons)) -> c15(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c15(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(min, cons)) -> c15(APP(min, cons), ENCARG(min)) ENCARG(cons_app(del, cons)) -> c15(APP(del, cons), ENCARG(del)) ENCARG(cons_app(map, cons)) -> c15(APP(map, cons), ENCARG(map)) ENCARG(cons_app(filter, cons)) -> c15(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(filter2, cons)) -> c15(APP(filter2, cons), ENCARG(filter2)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: ENCARG(cons_app(del, cons)) -> c15(APP(del, cons), ENCARG(del)) ENCARG(cons_app(true, cons)) -> c15(APP(true, cons), ENCARG(true)) ENCARG(cons_app(minsort, cons)) -> c15(APP(minsort, cons), ENCARG(minsort)) ENCARG(cons_app(s, cons)) -> c15(APP(s, cons), ENCARG(s)) ENCARG(cons_app(false, cons)) -> c15(APP(false, cons), ENCARG(false)) ENCARG(cons_app(0, cons)) -> c15(APP(0, cons), ENCARG(0)) ENCARG(cons_app(filter, cons)) -> c15(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(map, cons)) -> c15(APP(map, cons), ENCARG(map)) ENCARG(cons_app(le, cons)) -> c15(APP(le, cons), ENCARG(le)) ENCARG(cons_app(nil, cons)) -> c15(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c15(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(min, cons)) -> c15(APP(min, cons), ENCARG(min)) ENCARG(cons_app(eq, cons)) -> c15(APP(eq, cons), ENCARG(eq)) ENCARG(cons_app(filter2, cons)) -> c15(APP(filter2, cons), ENCARG(filter2)) ENCARG(cons_app(if, cons)) -> c15(APP(if, cons), ENCARG(if)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(le) -> le encArg(0) -> 0 encArg(true) -> true encArg(s) -> s encArg(false) -> false encArg(eq) -> eq encArg(if) -> if encArg(minsort) -> minsort encArg(nil) -> nil encArg(cons) -> cons encArg(min) -> min encArg(del) -> del encArg(map) -> map encArg(filter) -> filter encArg(filter2) -> filter2 encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(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(eq, 0), 0) -> true app(app(eq, 0), app(s, z0)) -> false app(app(eq, app(s, z0)), 0) -> false app(app(eq, app(s, z0)), app(s, z1)) -> app(app(eq, z0), z1) app(app(app(if, true), z0), z1) -> z0 app(app(app(if, false), z0), z1) -> z1 app(minsort, nil) -> nil app(minsort, app(app(cons, z0), z1)) -> app(app(cons, app(app(min, z0), z1)), app(minsort, app(app(del, app(app(min, z0), z1)), app(app(cons, z0), z1)))) app(app(min, z0), nil) -> z0 app(app(min, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2)) app(app(del, z0), nil) -> nil app(app(del, z0), app(app(cons, z1), z2)) -> app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))) 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(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, min)) -> c15(APP(encArg(x0), min), ENCARG(x0)) ENCARG(cons_app(x0, del)) -> c15(APP(encArg(x0), del), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c15(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c15(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c15(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(le, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(0, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(s, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(eq, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(if, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(minsort, x1)) -> c15(APP(minsort, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(min, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(del, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c15(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c15(ENCARG(x1)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, le) -> c(APP(encArg(x0), le)) ENCODE_APP(x0, 0) -> c(APP(encArg(x0), 0)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, s) -> c(APP(encArg(x0), s)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, eq) -> c(APP(encArg(x0), eq)) ENCODE_APP(x0, if) -> c(APP(encArg(x0), if)) ENCODE_APP(x0, minsort) -> c(APP(encArg(x0), minsort)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, min) -> c(APP(encArg(x0), min)) ENCODE_APP(x0, del) -> c(APP(encArg(x0), del)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) 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(minsort, x1) -> c(APP(minsort, 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, le))) -> c15(APP(encArg(x0), app(encArg(x1), le)), ENCARG(x0), ENCARG(cons_app(x1, le))) ENCARG(cons_app(x0, cons_app(x1, 0))) -> c15(APP(encArg(x0), app(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_app(x1, 0))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c15(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, s))) -> c15(APP(encArg(x0), app(encArg(x1), s)), ENCARG(x0), ENCARG(cons_app(x1, s))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c15(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, eq))) -> c15(APP(encArg(x0), app(encArg(x1), eq)), ENCARG(x0), ENCARG(cons_app(x1, eq))) ENCARG(cons_app(x0, cons_app(x1, if))) -> c15(APP(encArg(x0), app(encArg(x1), if)), ENCARG(x0), ENCARG(cons_app(x1, if))) ENCARG(cons_app(x0, cons_app(x1, minsort))) -> c15(APP(encArg(x0), app(encArg(x1), minsort)), ENCARG(x0), ENCARG(cons_app(x1, minsort))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c15(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c15(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, min))) -> c15(APP(encArg(x0), app(encArg(x1), min)), ENCARG(x0), ENCARG(cons_app(x1, min))) ENCARG(cons_app(x0, cons_app(x1, del))) -> c15(APP(encArg(x0), app(encArg(x1), del)), ENCARG(x0), ENCARG(cons_app(x1, del))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c15(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c15(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c15(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)))) -> c15(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(le, x2))) -> c15(APP(encArg(x0), app(le, encArg(x2))), ENCARG(x0), ENCARG(cons_app(le, x2))) ENCARG(cons_app(x0, cons_app(0, x2))) -> c15(APP(encArg(x0), app(0, encArg(x2))), ENCARG(x0), ENCARG(cons_app(0, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c15(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(s, x2))) -> c15(APP(encArg(x0), app(s, encArg(x2))), ENCARG(x0), ENCARG(cons_app(s, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c15(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(eq, x2))) -> c15(APP(encArg(x0), app(eq, encArg(x2))), ENCARG(x0), ENCARG(cons_app(eq, x2))) ENCARG(cons_app(x0, cons_app(if, x2))) -> c15(APP(encArg(x0), app(if, encArg(x2))), ENCARG(x0), ENCARG(cons_app(if, x2))) ENCARG(cons_app(x0, cons_app(minsort, x2))) -> c15(APP(encArg(x0), app(minsort, encArg(x2))), ENCARG(x0), ENCARG(cons_app(minsort, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c15(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c15(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(min, x2))) -> c15(APP(encArg(x0), app(min, encArg(x2))), ENCARG(x0), ENCARG(cons_app(min, x2))) ENCARG(cons_app(x0, cons_app(del, x2))) -> c15(APP(encArg(x0), app(del, encArg(x2))), ENCARG(x0), ENCARG(cons_app(del, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c15(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c15(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c15(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))) -> c15(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))) -> c15(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(le, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(0, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(s, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(eq, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(if, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(minsort, cons_app(x1, x2))) -> c15(APP(minsort, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(min, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(del, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c15(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, le), x2)) -> c15(APP(app(encArg(x0), le), encArg(x2)), ENCARG(cons_app(x0, le)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 0), x2)) -> c15(APP(app(encArg(x0), 0), encArg(x2)), ENCARG(cons_app(x0, 0)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c15(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, s), x2)) -> c15(APP(app(encArg(x0), s), encArg(x2)), ENCARG(cons_app(x0, s)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c15(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, eq), x2)) -> c15(APP(app(encArg(x0), eq), encArg(x2)), ENCARG(cons_app(x0, eq)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, if), x2)) -> c15(APP(app(encArg(x0), if), encArg(x2)), ENCARG(cons_app(x0, if)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, minsort), x2)) -> c15(APP(app(encArg(x0), minsort), encArg(x2)), ENCARG(cons_app(x0, minsort)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c15(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c15(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, min), x2)) -> c15(APP(app(encArg(x0), min), encArg(x2)), ENCARG(cons_app(x0, min)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, del), x2)) -> c15(APP(app(encArg(x0), del), encArg(x2)), ENCARG(cons_app(x0, del)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c15(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c15(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c15(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)) -> c15(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(le, x1), x2)) -> c15(APP(app(le, encArg(x1)), encArg(x2)), ENCARG(cons_app(le, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(eq, x1), x2)) -> c15(APP(app(eq, encArg(x1)), encArg(x2)), ENCARG(cons_app(eq, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(minsort, x1), x2)) -> c15(APP(app(minsort, encArg(x1)), encArg(x2)), ENCARG(cons_app(minsort, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(min, x1), x2)) -> c15(APP(app(min, encArg(x1)), encArg(x2)), ENCARG(cons_app(min, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(del, x1), x2)) -> c15(APP(app(del, encArg(x1)), encArg(x2)), ENCARG(cons_app(del, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c15(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c15(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)) -> c15(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), le)) -> c15(APP(app(encArg(x0), encArg(x1)), le), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 0)) -> c15(APP(app(encArg(x0), encArg(x1)), 0), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c15(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), s)) -> c15(APP(app(encArg(x0), encArg(x1)), s), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c15(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), eq)) -> c15(APP(app(encArg(x0), encArg(x1)), eq), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), if)) -> c15(APP(app(encArg(x0), encArg(x1)), if), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), minsort)) -> c15(APP(app(encArg(x0), encArg(x1)), minsort), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c15(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c15(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), min)) -> c15(APP(app(encArg(x0), encArg(x1)), min), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), del)) -> c15(APP(app(encArg(x0), encArg(x1)), del), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c15(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c15(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c15(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(0, x1), x2)) -> c15(ENCARG(cons_app(0, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c15(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(s, x1), x2)) -> c15(ENCARG(cons_app(s, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c15(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(if, x1), x2)) -> c15(ENCARG(cons_app(if, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c15(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c15(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c15(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(minsort, nil)) -> c15(APP(minsort, nil)) S tuples: APP(app(le, 0), z0) -> c32 APP(app(le, app(s, z0)), 0) -> c33 APP(app(eq, 0), 0) -> c35 APP(app(eq, 0), app(s, z0)) -> c36 APP(app(eq, app(s, z0)), 0) -> c37 APP(app(app(if, true), z0), z1) -> c39 APP(app(app(if, false), z0), z1) -> c40 APP(minsort, nil) -> c41 APP(app(min, z0), nil) -> c43 APP(app(del, z0), nil) -> c45 APP(app(map, z0), nil) -> c47 APP(app(filter, z0), nil) -> c49 APP(app(le, app(s, z0)), app(s, z1)) -> c34(APP(app(le, z0), z1)) APP(app(eq, app(s, z0)), app(s, z1)) -> c38(APP(app(eq, z0), z1)) APP(app(map, z0), app(app(cons, z1), z2)) -> c48(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c51(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c52(APP(app(filter, z0), z2)) APP(minsort, app(app(cons, z1), z2)) -> c42(APP(app(min, z1), z2), APP(minsort, app(app(app(if, app(app(eq, app(app(min, z1), z2)), z1)), z2), app(app(cons, z1), app(app(del, app(app(min, z1), z2)), z2)))), APP(app(del, app(app(min, z1), z2)), app(app(cons, z1), z2)), APP(app(min, z1), z2)) APP(minsort, app(app(cons, z0), nil)) -> c42(APP(app(min, z0), nil), APP(minsort, app(app(del, z0), app(app(cons, z0), nil))), APP(app(del, app(app(min, z0), nil)), app(app(cons, z0), nil)), APP(app(min, z0), nil)) APP(minsort, app(app(cons, z0), app(app(cons, z1), z2))) -> c42(APP(app(min, z0), app(app(cons, z1), z2)), APP(minsort, app(app(del, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2)))), APP(app(del, app(app(min, z0), app(app(cons, z1), z2))), app(app(cons, z0), app(app(cons, z1), z2))), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, x0), app(app(cons, z0), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), app(app(cons, z1), z2))), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), APP(app(le, x0), z0), APP(app(min, x0), app(app(cons, z1), z2)), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(min, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c44(APP(app(app(if, app(app(le, z0), x1)), app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(app(min, x1), app(app(cons, z1), z2))), APP(app(le, z0), x1), APP(app(min, z0), app(app(cons, z1), z2)), APP(app(min, x1), app(app(cons, z1), z2))) APP(app(min, 0), app(app(cons, z0), x2)) -> c44(APP(app(app(if, true), app(app(min, 0), x2)), app(app(min, z0), x2)), APP(app(le, 0), z0), APP(app(min, 0), x2), APP(app(min, z0), x2)) APP(app(min, app(s, z0)), app(app(cons, 0), x2)) -> c44(APP(app(app(if, false), app(app(min, app(s, z0)), x2)), app(app(min, 0), x2)), APP(app(le, app(s, z0)), 0), APP(app(min, app(s, z0)), x2), APP(app(min, 0), x2)) APP(app(min, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c44(APP(app(app(if, app(app(le, z0), z1)), app(app(min, app(s, z0)), x2)), app(app(min, app(s, z1)), x2)), APP(app(le, app(s, z0)), app(s, z1)), APP(app(min, app(s, z0)), x2), APP(app(min, app(s, z1)), x2)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(app(if, app(app(le, x0), z0)), app(app(min, x0), nil)), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(le, x0), z0)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, x0), nil)) APP(app(min, x0), app(app(cons, z0), nil)) -> c1(APP(app(min, z0), nil)) APP(app(min, z0), app(app(cons, x1), nil)) -> c1(APP(app(app(if, app(app(le, z0), x1)), z0), app(app(min, x1), nil))) APP(app(del, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c46(APP(app(app(if, app(app(eq, z0), x1)), app(app(cons, z1), z2)), app(app(cons, x1), app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2))))), APP(app(eq, z0), x1), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(del, 0), app(app(cons, 0), x2)) -> c46(APP(app(app(if, true), x2), app(app(cons, 0), app(app(del, 0), x2))), APP(app(eq, 0), 0), APP(app(del, 0), x2)) APP(app(del, 0), app(app(cons, app(s, z0)), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, app(s, z0)), app(app(del, 0), x2))), APP(app(eq, 0), app(s, z0)), APP(app(del, 0), x2)) APP(app(del, app(s, z0)), app(app(cons, 0), x2)) -> c46(APP(app(app(if, false), x2), app(app(cons, 0), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), 0), APP(app(del, app(s, z0)), x2)) APP(app(del, app(s, z0)), app(app(cons, app(s, z1)), x2)) -> c46(APP(app(app(if, app(app(eq, z0), z1)), x2), app(app(cons, app(s, z1)), app(app(del, app(s, z0)), x2))), APP(app(eq, app(s, z0)), app(s, z1)), APP(app(del, app(s, z0)), x2)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(app(if, app(app(eq, z0), x1)), nil), app(app(cons, x1), nil))) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(eq, z0), x1)) APP(app(del, z0), app(app(cons, x1), nil)) -> c2(APP(app(del, z0), nil)) APP(app(filter, app(le, 0)), app(app(cons, z0), x2)) -> c50(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)) -> c50(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)) -> c50(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(eq, 0)), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, true), app(eq, 0)), 0), x2), APP(app(eq, 0), 0)) APP(app(filter, app(eq, 0)), app(app(cons, app(s, z0)), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, 0)), app(s, z0)), x2), APP(app(eq, 0), app(s, z0))) APP(app(filter, app(eq, app(s, z0))), app(app(cons, 0), x2)) -> c50(APP(app(app(app(filter2, false), app(eq, app(s, z0))), 0), x2), APP(app(eq, app(s, z0)), 0)) APP(app(filter, app(eq, app(s, z0))), app(app(cons, app(s, z1)), x2)) -> c50(APP(app(app(app(filter2, app(app(eq, z0), z1)), app(eq, app(s, z0))), app(s, z1)), x2), APP(app(eq, app(s, z0)), app(s, z1))) APP(app(filter, app(app(if, true), z0)), app(app(cons, z1), x2)) -> c50(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)) -> c50(APP(app(app(app(filter2, z1), app(app(if, false), z0)), z1), x2), APP(app(app(if, false), z0), z1)) APP(app(filter, app(min, z0)), app(app(cons, nil), x2)) -> c50(APP(app(app(app(filter2, z0), app(min, z0)), nil), x2), APP(app(min, z0), nil)) APP(app(filter, app(min, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(le, z0), z1)), app(app(min, z0), z2)), app(app(min, z1), z2))), app(min, z0)), app(app(cons, z1), z2)), x2), APP(app(min, z0), app(app(cons, z1), z2))) APP(app(filter, app(del, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(app(app(filter2, app(app(app(if, app(app(eq, z0), z1)), z2), app(app(cons, z1), app(app(del, z0), z2)))), app(del, z0)), app(app(cons, z1), z2)), x2), APP(app(del, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(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)) -> c50(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, minsort), app(app(cons, nil), x2)) -> c50(APP(minsort, nil)) APP(app(filter, minsort), app(app(cons, app(app(cons, z0), z1)), x2)) -> c50(APP(minsort, app(app(cons, z0), z1))) APP(app(filter, app(del, z0)), app(app(cons, nil), x2)) -> c50(APP(app(del, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c50(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c50(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c50(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c50(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: c32, c33, c35, c36, c37, c39, c40, c41, c43, c45, c47, c49, c34_1, c38_1, c48_2, c51_1, c52_1, c15_2, c15_1, c42_4, c44_4, c1_1, c46_3, c2_1, c50_2, c50_1, c_1, c15_3